BACKGROUND Many cases of emphysema associated with blow-out fractures occur before surgery due to trauma.However,emphysema can occur even after surgery,and most of such cases are managed conservatively and allowed to ...BACKGROUND Many cases of emphysema associated with blow-out fractures occur before surgery due to trauma.However,emphysema can occur even after surgery,and most of such cases are managed conservatively and allowed to resolve.Swelling in the periorbital area due to emphysema that occurs after surgery can make early recovery difficult.CASE SUMMARY Herein,we describe a case of postoperative subcutaneous emphysema that was treated using a simple needle aspiration method.A 48-year-old male patient visited the hospital with a blow-out fracture of the left medial orbital wall and nasal bone fracture.One day postoperatively,swelling and crepitus in the left periorbital area were observed,and follow-up computed tomography showed emphysema in the left periorbital subcutaneous area.Needle aspiration using an 18-gauge needle and syringe was used to relieve the emphysema.The symptoms of sudden swelling improved immediately,and no recurrence was observed.CONCLUSION We conclude that needle aspiration is a useful method that could help in relieving symptom,resolving discomfort,and enabling early return to daily life in patients with postoperative subcutaneous emphysema.展开更多
The amount of oxygen blown into the converter is one of the key parameters for the control of the converter blowing process,which directly affects the tap-to-tap time of converter. In this study, a hybrid model based ...The amount of oxygen blown into the converter is one of the key parameters for the control of the converter blowing process,which directly affects the tap-to-tap time of converter. In this study, a hybrid model based on oxygen balance mechanism (OBM) and deep neural network (DNN) was established for predicting oxygen blowing time in converter. A three-step method was utilized in the hybrid model. First, the oxygen consumption volume was predicted by the OBM model and DNN model, respectively. Second, a more accurate oxygen consumption volume was obtained by integrating the OBM model and DNN model. Finally, the converter oxygen blowing time was calculated according to the oxygen consumption volume and the oxygen supply intensity of each heat. The proposed hybrid model was verified using the actual data collected from an integrated steel plant in China, and compared with multiple linear regression model, OBM model, and neural network model including extreme learning machine, back propagation neural network, and DNN. The test results indicate that the hybrid model with a network structure of 3 hidden layer layers, 32-16-8 neurons per hidden layer, and 0.1 learning rate has the best prediction accuracy and stronger generalization ability compared with other models. The predicted hit ratio of oxygen consumption volume within the error±300 m^(3)is 96.67%;determination coefficient (R^(2)) and root mean square error (RMSE) are0.6984 and 150.03 m^(3), respectively. The oxygen blow time prediction hit ratio within the error±0.6 min is 89.50%;R2and RMSE are0.9486 and 0.3592 min, respectively. As a result, the proposed model can effectively predict the oxygen consumption volume and oxygen blowing time in the converter.展开更多
This article discusses and analyzes the law of nitrogen increase in liquid steel and the main factors affect-ing the nitrogen increasing of molten steel,through the way of adding nitrogen to molten steel by bottom blo...This article discusses and analyzes the law of nitrogen increase in liquid steel and the main factors affect-ing the nitrogen increasing of molten steel,through the way of adding nitrogen to molten steel by bottom blowing nitrogen gas in LF refining process.It is considered that the main factors affecting the nitrogen increasing instability of molten steel are the initial temperature of LF refining,nitrogen relative element,surface active elements[O]and[S]of steel liquid,and bottom blowing rate of ladle.The large-scale production practice shows that T[O]not more than 50×10-6 and[S]is not more than 0.020 in LF refining at the initial temperature of not less than 1570.The liquid steel nitrogen enrichment test is carried out by ladle bottom blowing nitrogen gas after 20 min of refining,the flow rate is set as(6.0~7.0)NL/min per ton,and it is turned to 2 NL/min at 6 min before the end of refining,the nitrogen increasing rate of liquid steel is basically stable at(5~6)×10-6 per minute.展开更多
Currently, many studies have been made for years on dimensions of pneumatic nozzle, which influence the flow characteristic of blowing system. For the purpose of outputting the same blowing force, the supply pressure ...Currently, many studies have been made for years on dimensions of pneumatic nozzle, which influence the flow characteristic of blowing system. For the purpose of outputting the same blowing force, the supply pressure could be reduced by decreasing the ratio of length to diameter of nozzle. The friction between high speed air and pipe wall would be reduced if the nozzle is designed to be converging shape comparing with straight shape. But the volume flow and pressure, discussed in these studies, do not describe energy loss of the blowing system directly. Pneumatic power is an innovative principle to estimate pneumatic system’s energy consumption directly. Based on the above principle, a pulse blowing method is put forward for saving energy. A flow experiment is carried out, in which the high speed air flows from the pulse blowing system and continuous blowing system respectively to a plate with grease on top. Supply pressure and the volume of air used for removing the grease are measured to calculate energy consumption. From the experiment result, the pulse blowing system performs to conserve energy comparing with the continuous blowing system. The frequency and duty ratio of pulse flow influence the blowing characteristic. The pulse blowing system performs to be the most efficient at the specified frequency and duty ratio. Then a pneumatic self-oscillated method based on air operated valve is put forward to generate pulse flow. A simulation is made about dynamic modeling the air operated valve and calculating the motion of the valve core and output pressure. The simulation result verifies the system to be able to generate pulse flow, and predicts the key parameters of the frequency and duty ratio measured by experiment well. Finally, on the basis of simplifying and solution of the pulse blowing system’s mathematic model, the relationship between system’s frequency duty ratio and the dimensions of components is simply described with four algebraic equations. The system could be designed with specified frequency and duty ratio according to the four equations. This study provides theoretical basis for designing energy-saving air blowing system.展开更多
Li et al. in [3] obtained blow-up results for a system of Petrovskey equations in some different cases. In this article we obtain lower bounds for the blow up time under some considerations on initial data.
A three-dimensional mathematical model was developed to investigate the effect of gas blowing nozzle angles on multiphase flow,circulation flow rate,and mixing time during Ruhrstahl-Heraeus(RH) refining process.Also,a...A three-dimensional mathematical model was developed to investigate the effect of gas blowing nozzle angles on multiphase flow,circulation flow rate,and mixing time during Ruhrstahl-Heraeus(RH) refining process.Also,a water model with a geometric scale of 1:4 from an industrial RH furnace of 260 t was built up,and measurements were carried out to validate the mathematical model.The results show that,with a conventional gas blowing nozzle and the total gas flow rate of 40 L·min^(-1),the mixing time predicted by the mathematical model agrees well with the measured values.The deviations between the model predictions and the measured values are in the range of about 1.3%–7.3% at the selected three monitoring locations,where the mixing time was defined as the required time when the dimensionless concentration is within 3% deviation from the bath averaged value.In addition,the circulation flow rate was 9 kg·s^(-1).When the gas blowing nozzle was horizontally rotated by either 30° or 45°,the circulation flow rate was found to be increased by about 15% compared to a conventional nozzle,due to the rotational flow formed in the up-snorkel.Furthermore,the mixing time at the monitoring point 1,2,and 3 was shortened by around 21.3%,28.2%,and 12.3%,respectively.With the nozzle angle of 30° and 45°,the averaged residence time of 128 bubbles in liquid was increased by around 33.3%.展开更多
In this paper we deal with the initial boundary value problem for two classes of reaction diffusion systems with two source terms in bounded domain. Under some assumptions on the exponents and the initial data, applyi...In this paper we deal with the initial boundary value problem for two classes of reaction diffusion systems with two source terms in bounded domain. Under some assumptions on the exponents and the initial data, applying the comparison principle, the maximum prin- ciple and the supersolution-subsolution method, we prove the global existence and blow up of solutions. We also establish some upper blow up rates.展开更多
Gas blowout is one of the major hazard in petroleum field which normally damages the gas bearing geologic formation, structure, local tectonic setting, environment and so on. In Bangladesh, there have been three well ...Gas blowout is one of the major hazard in petroleum field which normally damages the gas bearing geologic formation, structure, local tectonic setting, environment and so on. In Bangladesh, there have been three well known gas blowouts. Among them, the most dangerous gas well blowout took place on 8 January 2005 in Sunamganj district when chattak-2 (also known as Tengratila) gas field was drilled. As a result, the surrounding area is facing various problems among them water is the top of the list. From this point of view, the present study has been considered to find the impact of blowout on water around the gas blowout area. In this regard, the water samples (some are very near and some are away from the well) are collected and analyzed in the laboratory following the standard method. Some physical and chemical parameters of water such as pH, turbidity, EC, total solids, dissolved solids, suspended solids, manganese ion, calcium ion, magnesium, iron, chloride and total hardness have measured where without turbidity, manganese and iron, all are still in tolerable state for all purposes and ranging within standard limit based on WHO, EU and EQS for Bangladesh. The quality of the near well tube wells water is much decreased than far away tube wells water which might be the direct or indirect influence of the blowout incident around the area.展开更多
For the nonlinear wave equation in R-N x R+ (N greater than or equal to 2): partial derivative(2)u(x,t)/partial derivative(t)(2) - a partial derivative/partial derivative(xi)(a/(x) partial derivative/partial derivativ...For the nonlinear wave equation in R-N x R+ (N greater than or equal to 2): partial derivative(2)u(x,t)/partial derivative(t)(2) - a partial derivative/partial derivative(xi)(a/(x) partial derivative/partial derivative(xi)u) = \u\(p-1 u,) in 1980 Kato proved the solution of Cauchy problem may blow rtp infinite time if 1 < p less than or equal to N + 1/N - 1. In the present work his result allowing 1 < p less than or equal to N + 3/N - 1 is improved by using different estimates.展开更多
Through systematical experiment design, the physical blowing agent(PBA) mass loss of bio-based polyurethane rigid foam(PURF)in the foaming process was measured and calculated in this study, and different eco-friendly ...Through systematical experiment design, the physical blowing agent(PBA) mass loss of bio-based polyurethane rigid foam(PURF)in the foaming process was measured and calculated in this study, and different eco-friendly PBA mass losses were measured quantitatively for the first time. The core of the proposed method is to add water to replace the difference, and this method has a high fault tolerance rate for different foaming forms of foams. The method was proved to be stable and reliable through the standard deviations σ1and σ2for R1(ratio of the PBA mass loss to the material total mass except the PBA) and R2(ratio of the PBA mass loss to the PBA mass in the material total mass) in parallel experiments. It can be used to measure and calculate the actual PBA mass loss in the foaming process of both bio-based and petroleumbased PURF. The results show that the PBA mass loss in PURF with different PBA systems is controlled by its initial mass content of PBA in PU materials ω. The main way for PBA to dissipate into the air is evaporation/escape along the upper surface of foam. This study further reveals the mechanism of PBA mass loss: the evaporation/escape of PBA along the upper surface of foam is a typical diffusion behavior. Its spread power comes from the difference between the chemical potential of PBA in the interface layer and that in the outside air. For a certain PURF system, R1has approximately linear relationship with the initial mass content of PBA in PU materials ω, which can be expressed by the functional relationship R1= kω, where k is a variable related to PBA’s own attributes.展开更多
Cryogenic insulation material rigid polyurethane(PU)foams were developed using bio-based and recycled feedstock.Polyols obtained from tall oil fatty acids produced as a side stream of wood biomass pulping and recycled...Cryogenic insulation material rigid polyurethane(PU)foams were developed using bio-based and recycled feedstock.Polyols obtained from tall oil fatty acids produced as a side stream of wood biomass pulping and recycled polyethylene terephthalate were used to develop rigid PU foam formulations.The 4th generation physical blowing agents with low global warming potential and low ozone depletion potential were used to develop rigid PU foam cryogenic insulation with excellent mechanical and thermal properties.Obtained rigid PU foams had a thermal conductivity coefficient as low as 0.0171 W/m·K and an apparent density of 37-40 kg/m^(3).The developed rigid PU foams had anisotropic compression strength properties,which were higher parallel to the foaming direction.Moreover,the compression strength was also influenced by the type of applied bio-based polyol.The bio-based polyols with higher OH group functionality delivered higher crosslinking density of polymer matrix;thus,the mechanical properties were also higher.The mechanical strength of the foams increased when materials were tested at liquid nitrogen temperature due to the stiffening of the polymer matrix.The thermal properties of the developed materials were determined using differential scanning calorimetry,dynamic mechanical analysis,and thermogravimetric analysis methods.Lastly,the developed rigid PU foams had good adhesion to the aluminium substrate before and after applying cyroshock and an excellent safety coefficient of 4-5.Rigid PU foams developed using Solstice LBA delivered adhesion strength of~0.5 MPa and may be considered for application as cryogenic insulation in the aerospace industry.展开更多
We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy leve...We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy level. Then, we establish the existence of solutions blowing up in finite time with initial data at arbitrary energy level. Finally, we estimate the upper bound of the blow-up time under certain conditions.展开更多
基金Supported by Soonchunhyang research fund,No.2023-0024.
文摘BACKGROUND Many cases of emphysema associated with blow-out fractures occur before surgery due to trauma.However,emphysema can occur even after surgery,and most of such cases are managed conservatively and allowed to resolve.Swelling in the periorbital area due to emphysema that occurs after surgery can make early recovery difficult.CASE SUMMARY Herein,we describe a case of postoperative subcutaneous emphysema that was treated using a simple needle aspiration method.A 48-year-old male patient visited the hospital with a blow-out fracture of the left medial orbital wall and nasal bone fracture.One day postoperatively,swelling and crepitus in the left periorbital area were observed,and follow-up computed tomography showed emphysema in the left periorbital subcutaneous area.Needle aspiration using an 18-gauge needle and syringe was used to relieve the emphysema.The symptoms of sudden swelling improved immediately,and no recurrence was observed.CONCLUSION We conclude that needle aspiration is a useful method that could help in relieving symptom,resolving discomfort,and enabling early return to daily life in patients with postoperative subcutaneous emphysema.
基金financially supported by the National Natural Science Foundation of China (Nos.51974023 and52374321)the funding of State Key Laboratory of Advanced Metallurgy,University of Science and Technology Beijing,China (No.41620007)。
文摘The amount of oxygen blown into the converter is one of the key parameters for the control of the converter blowing process,which directly affects the tap-to-tap time of converter. In this study, a hybrid model based on oxygen balance mechanism (OBM) and deep neural network (DNN) was established for predicting oxygen blowing time in converter. A three-step method was utilized in the hybrid model. First, the oxygen consumption volume was predicted by the OBM model and DNN model, respectively. Second, a more accurate oxygen consumption volume was obtained by integrating the OBM model and DNN model. Finally, the converter oxygen blowing time was calculated according to the oxygen consumption volume and the oxygen supply intensity of each heat. The proposed hybrid model was verified using the actual data collected from an integrated steel plant in China, and compared with multiple linear regression model, OBM model, and neural network model including extreme learning machine, back propagation neural network, and DNN. The test results indicate that the hybrid model with a network structure of 3 hidden layer layers, 32-16-8 neurons per hidden layer, and 0.1 learning rate has the best prediction accuracy and stronger generalization ability compared with other models. The predicted hit ratio of oxygen consumption volume within the error±300 m^(3)is 96.67%;determination coefficient (R^(2)) and root mean square error (RMSE) are0.6984 and 150.03 m^(3), respectively. The oxygen blow time prediction hit ratio within the error±0.6 min is 89.50%;R2and RMSE are0.9486 and 0.3592 min, respectively. As a result, the proposed model can effectively predict the oxygen consumption volume and oxygen blowing time in the converter.
文摘This article discusses and analyzes the law of nitrogen increase in liquid steel and the main factors affect-ing the nitrogen increasing of molten steel,through the way of adding nitrogen to molten steel by bottom blowing nitrogen gas in LF refining process.It is considered that the main factors affecting the nitrogen increasing instability of molten steel are the initial temperature of LF refining,nitrogen relative element,surface active elements[O]and[S]of steel liquid,and bottom blowing rate of ladle.The large-scale production practice shows that T[O]not more than 50×10-6 and[S]is not more than 0.020 in LF refining at the initial temperature of not less than 1570.The liquid steel nitrogen enrichment test is carried out by ladle bottom blowing nitrogen gas after 20 min of refining,the flow rate is set as(6.0~7.0)NL/min per ton,and it is turned to 2 NL/min at 6 min before the end of refining,the nitrogen increasing rate of liquid steel is basically stable at(5~6)×10-6 per minute.
文摘Currently, many studies have been made for years on dimensions of pneumatic nozzle, which influence the flow characteristic of blowing system. For the purpose of outputting the same blowing force, the supply pressure could be reduced by decreasing the ratio of length to diameter of nozzle. The friction between high speed air and pipe wall would be reduced if the nozzle is designed to be converging shape comparing with straight shape. But the volume flow and pressure, discussed in these studies, do not describe energy loss of the blowing system directly. Pneumatic power is an innovative principle to estimate pneumatic system’s energy consumption directly. Based on the above principle, a pulse blowing method is put forward for saving energy. A flow experiment is carried out, in which the high speed air flows from the pulse blowing system and continuous blowing system respectively to a plate with grease on top. Supply pressure and the volume of air used for removing the grease are measured to calculate energy consumption. From the experiment result, the pulse blowing system performs to conserve energy comparing with the continuous blowing system. The frequency and duty ratio of pulse flow influence the blowing characteristic. The pulse blowing system performs to be the most efficient at the specified frequency and duty ratio. Then a pneumatic self-oscillated method based on air operated valve is put forward to generate pulse flow. A simulation is made about dynamic modeling the air operated valve and calculating the motion of the valve core and output pressure. The simulation result verifies the system to be able to generate pulse flow, and predicts the key parameters of the frequency and duty ratio measured by experiment well. Finally, on the basis of simplifying and solution of the pulse blowing system’s mathematic model, the relationship between system’s frequency duty ratio and the dimensions of components is simply described with four algebraic equations. The system could be designed with specified frequency and duty ratio according to the four equations. This study provides theoretical basis for designing energy-saving air blowing system.
文摘Li et al. in [3] obtained blow-up results for a system of Petrovskey equations in some different cases. In this article we obtain lower bounds for the blow up time under some considerations on initial data.
基金financially supported by the National Natural Science Foundation of China(No.51704062)the Fundamental Research Funds for the Central Universities,China(No.N2025019)。
文摘A three-dimensional mathematical model was developed to investigate the effect of gas blowing nozzle angles on multiphase flow,circulation flow rate,and mixing time during Ruhrstahl-Heraeus(RH) refining process.Also,a water model with a geometric scale of 1:4 from an industrial RH furnace of 260 t was built up,and measurements were carried out to validate the mathematical model.The results show that,with a conventional gas blowing nozzle and the total gas flow rate of 40 L·min^(-1),the mixing time predicted by the mathematical model agrees well with the measured values.The deviations between the model predictions and the measured values are in the range of about 1.3%–7.3% at the selected three monitoring locations,where the mixing time was defined as the required time when the dimensionless concentration is within 3% deviation from the bath averaged value.In addition,the circulation flow rate was 9 kg·s^(-1).When the gas blowing nozzle was horizontally rotated by either 30° or 45°,the circulation flow rate was found to be increased by about 15% compared to a conventional nozzle,due to the rotational flow formed in the up-snorkel.Furthermore,the mixing time at the monitoring point 1,2,and 3 was shortened by around 21.3%,28.2%,and 12.3%,respectively.With the nozzle angle of 30° and 45°,the averaged residence time of 128 bubbles in liquid was increased by around 33.3%.
基金supported by the National Natural Science Foundation of China(11471087)the China Postdoctoral Science Foundation(2013M540270)+1 种基金the Heilongjiang Postdoctoral Foundation(LBH-Z13056,LBHZ15036)the Fundamental Research Funds for the Central Universities
文摘In this paper we deal with the initial boundary value problem for two classes of reaction diffusion systems with two source terms in bounded domain. Under some assumptions on the exponents and the initial data, applying the comparison principle, the maximum prin- ciple and the supersolution-subsolution method, we prove the global existence and blow up of solutions. We also establish some upper blow up rates.
文摘Gas blowout is one of the major hazard in petroleum field which normally damages the gas bearing geologic formation, structure, local tectonic setting, environment and so on. In Bangladesh, there have been three well known gas blowouts. Among them, the most dangerous gas well blowout took place on 8 January 2005 in Sunamganj district when chattak-2 (also known as Tengratila) gas field was drilled. As a result, the surrounding area is facing various problems among them water is the top of the list. From this point of view, the present study has been considered to find the impact of blowout on water around the gas blowout area. In this regard, the water samples (some are very near and some are away from the well) are collected and analyzed in the laboratory following the standard method. Some physical and chemical parameters of water such as pH, turbidity, EC, total solids, dissolved solids, suspended solids, manganese ion, calcium ion, magnesium, iron, chloride and total hardness have measured where without turbidity, manganese and iron, all are still in tolerable state for all purposes and ranging within standard limit based on WHO, EU and EQS for Bangladesh. The quality of the near well tube wells water is much decreased than far away tube wells water which might be the direct or indirect influence of the blowout incident around the area.
基金the National Natural Science Foundation of China
文摘For the nonlinear wave equation in R-N x R+ (N greater than or equal to 2): partial derivative(2)u(x,t)/partial derivative(t)(2) - a partial derivative/partial derivative(xi)(a/(x) partial derivative/partial derivative(xi)u) = \u\(p-1 u,) in 1980 Kato proved the solution of Cauchy problem may blow rtp infinite time if 1 < p less than or equal to N + 1/N - 1. In the present work his result allowing 1 < p less than or equal to N + 3/N - 1 is improved by using different estimates.
文摘Through systematical experiment design, the physical blowing agent(PBA) mass loss of bio-based polyurethane rigid foam(PURF)in the foaming process was measured and calculated in this study, and different eco-friendly PBA mass losses were measured quantitatively for the first time. The core of the proposed method is to add water to replace the difference, and this method has a high fault tolerance rate for different foaming forms of foams. The method was proved to be stable and reliable through the standard deviations σ1and σ2for R1(ratio of the PBA mass loss to the material total mass except the PBA) and R2(ratio of the PBA mass loss to the PBA mass in the material total mass) in parallel experiments. It can be used to measure and calculate the actual PBA mass loss in the foaming process of both bio-based and petroleumbased PURF. The results show that the PBA mass loss in PURF with different PBA systems is controlled by its initial mass content of PBA in PU materials ω. The main way for PBA to dissipate into the air is evaporation/escape along the upper surface of foam. This study further reveals the mechanism of PBA mass loss: the evaporation/escape of PBA along the upper surface of foam is a typical diffusion behavior. Its spread power comes from the difference between the chemical potential of PBA in the interface layer and that in the outside air. For a certain PURF system, R1has approximately linear relationship with the initial mass content of PBA in PU materials ω, which can be expressed by the functional relationship R1= kω, where k is a variable related to PBA’s own attributes.
基金funded by projects“Smart Materials,Photonics,Technologies and Engineering Ecosystem(MOTE)”(Contract No.VPP-EM-FOTONIKA-2022/1-0001)“Bio-Based Cryogenic Insulation for Aerospace Application(BioSpace)”(Contract No.4000135271/21/NL/SC).
文摘Cryogenic insulation material rigid polyurethane(PU)foams were developed using bio-based and recycled feedstock.Polyols obtained from tall oil fatty acids produced as a side stream of wood biomass pulping and recycled polyethylene terephthalate were used to develop rigid PU foam formulations.The 4th generation physical blowing agents with low global warming potential and low ozone depletion potential were used to develop rigid PU foam cryogenic insulation with excellent mechanical and thermal properties.Obtained rigid PU foams had a thermal conductivity coefficient as low as 0.0171 W/m·K and an apparent density of 37-40 kg/m^(3).The developed rigid PU foams had anisotropic compression strength properties,which were higher parallel to the foaming direction.Moreover,the compression strength was also influenced by the type of applied bio-based polyol.The bio-based polyols with higher OH group functionality delivered higher crosslinking density of polymer matrix;thus,the mechanical properties were also higher.The mechanical strength of the foams increased when materials were tested at liquid nitrogen temperature due to the stiffening of the polymer matrix.The thermal properties of the developed materials were determined using differential scanning calorimetry,dynamic mechanical analysis,and thermogravimetric analysis methods.Lastly,the developed rigid PU foams had good adhesion to the aluminium substrate before and after applying cyroshock and an excellent safety coefficient of 4-5.Rigid PU foams developed using Solstice LBA delivered adhesion strength of~0.5 MPa and may be considered for application as cryogenic insulation in the aerospace industry.
基金Supported by National Natural Science Foundation of China(Grant No.11801145)the Innovative Funds Plan of Henan University of Technology(Grant No.2020ZKCJ09)。
文摘We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy level. Then, we establish the existence of solutions blowing up in finite time with initial data at arbitrary energy level. Finally, we estimate the upper bound of the blow-up time under certain conditions.
