在以计算机技术、物联网(Internet of Things,IoT)技术、云存储技术以及智能机器人等为核心的智能化时代,输配电网络正发生着深刻的变化,其中输配电网络的智能化远程控制成为今后的重要发展趋势。为了做好电力物联网系统中避雷设备的远...在以计算机技术、物联网(Internet of Things,IoT)技术、云存储技术以及智能机器人等为核心的智能化时代,输配电网络正发生着深刻的变化,其中输配电网络的智能化远程控制成为今后的重要发展趋势。为了做好电力物联网系统中避雷设备的远程监测和维护,提出一种结构简单、成本低廉且覆盖发电、输电、变电、配电、用电以及调度等的无线避雷设备,利用云计算、大数据、物联网等先进的技术实现全面化、专业化以及智能化的远程避雷信息服务。展开更多
This paper deals with the Cauchy problem to the nonlinear pseudo-parabolic system ut - △u - αut =vp, vt -△v - α△vt = uq with p, q≥ 1 and pq 〉 1, where the viscous terms of third order are included. We first fin...This paper deals with the Cauchy problem to the nonlinear pseudo-parabolic system ut - △u - αut =vp, vt -△v - α△vt = uq with p, q≥ 1 and pq 〉 1, where the viscous terms of third order are included. We first find the critical Fujita exponent, and then determine the second critical exponent to characterize the critical space-decay rate of initial data in the co-existence region of global and non-global solutions. Moreover, time-decay profiles are obtained for the global solutions. It can be found that, different from those for the situations of general semilinear heat systems, we have to use distinctive techniques to treat the influence from the viscous terms of the highest order. To fix the non-global solutions, we exploit the test function method, instead of the general Kaplan method for heat systems. To obtain the global solutions, we apply the LP-Lq technique to establish some uniform Lm time-decay estimates. In particular, under a suitable classification for the nonlinear parameters and the initial data, various Lm time-decay estimates in the procedure enable us to arrive at the time-decay profiles of solutions to the system. It is mentioned that the general scaling method for parabolic problems relies heavily on regularizing effect to establish the compactness of approximating solutions, which cannot be directly realized here due to absence of the smooth effect in the pseudo-parabolic system.展开更多
This paper studies a higher-order semilinear parabolic system. We obtain the second critical exponent to characterize the critical space-decay rate of the initial data in the co-existence parameter region of global an...This paper studies a higher-order semilinear parabolic system. We obtain the second critical exponent to characterize the critical space-decay rate of the initial data in the co-existence parameter region of global and non-global solutions. Together with the critical Fujita exponent established by Pang et al.(2006),this gives a clear and complete picture to the Fujita phenomena in the coupled higher-order semilinear parabolic system.展开更多
文摘在以计算机技术、物联网(Internet of Things,IoT)技术、云存储技术以及智能机器人等为核心的智能化时代,输配电网络正发生着深刻的变化,其中输配电网络的智能化远程控制成为今后的重要发展趋势。为了做好电力物联网系统中避雷设备的远程监测和维护,提出一种结构简单、成本低廉且覆盖发电、输电、变电、配电、用电以及调度等的无线避雷设备,利用云计算、大数据、物联网等先进的技术实现全面化、专业化以及智能化的远程避雷信息服务。
基金supported by National Natural Science Foundation of China(Grant Nos.11171048 and 11201047)the Doctor Startup Foundation of Liaoning Province(Grant No.20121025)the Fundamental Research Funds for the Central Universities
文摘This paper deals with the Cauchy problem to the nonlinear pseudo-parabolic system ut - △u - αut =vp, vt -△v - α△vt = uq with p, q≥ 1 and pq 〉 1, where the viscous terms of third order are included. We first find the critical Fujita exponent, and then determine the second critical exponent to characterize the critical space-decay rate of initial data in the co-existence region of global and non-global solutions. Moreover, time-decay profiles are obtained for the global solutions. It can be found that, different from those for the situations of general semilinear heat systems, we have to use distinctive techniques to treat the influence from the viscous terms of the highest order. To fix the non-global solutions, we exploit the test function method, instead of the general Kaplan method for heat systems. To obtain the global solutions, we apply the LP-Lq technique to establish some uniform Lm time-decay estimates. In particular, under a suitable classification for the nonlinear parameters and the initial data, various Lm time-decay estimates in the procedure enable us to arrive at the time-decay profiles of solutions to the system. It is mentioned that the general scaling method for parabolic problems relies heavily on regularizing effect to establish the compactness of approximating solutions, which cannot be directly realized here due to absence of the smooth effect in the pseudo-parabolic system.
基金supported by National Natural Science Foundation of China(Grant Nos.11171048 and 11326149)the Science and Technology Research Project of Department of Education of Jiangxi Province(Grant No.GJJ14759)
文摘This paper studies a higher-order semilinear parabolic system. We obtain the second critical exponent to characterize the critical space-decay rate of the initial data in the co-existence parameter region of global and non-global solutions. Together with the critical Fujita exponent established by Pang et al.(2006),this gives a clear and complete picture to the Fujita phenomena in the coupled higher-order semilinear parabolic system.
