We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a usef...The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a useful inequality is obtained, which can be used to derive the self-improving regularity.展开更多
In this paper,we consider solving numerically for the first time inverse problems of determining the time-dependent thermal diffusivity coefficient for a weakly degenerate heat equation,which vanishes at the initial m...In this paper,we consider solving numerically for the first time inverse problems of determining the time-dependent thermal diffusivity coefficient for a weakly degenerate heat equation,which vanishes at the initial moment of time,and/or the convection coefficient along with the temperature for a one-dimensional parabolic equation,from some additional information about the process(the so-called over-determination conditions).Although uniquely solvable these inverse problems are still ill-posed since small changes in the input data can result in enormous changes in the output solution.The finite difference method with the Crank-Nicolson scheme combined with the nonlinear Tikhonov regularization are employed.The resulting minimization problem is computationally solved using the MATLAB toolbox routine lsqnonlin.For both exact and noisy input data,accurate and stable numerical results are obtained.展开更多
It is obtained the existence of the weak solution for a degenerate generalized Burgers equation under the restriction u0 ∈ L∞. The main method is to add viscosity perturbation and obtain some estimates in L1 norm. M...It is obtained the existence of the weak solution for a degenerate generalized Burgers equation under the restriction u0 ∈ L∞. The main method is to add viscosity perturbation and obtain some estimates in L1 norm. Meanwhile it is obtained the solution is exponential decay when the initial data has compact support.展开更多
In this paper, the authors consider a system of degenerate Davey-Stewartson equations. They prove the global existence of weak solutions in some weighted function spaces and the decay of weak solutions in some anisotr...In this paper, the authors consider a system of degenerate Davey-Stewartson equations. They prove the global existence of weak solutions in some weighted function spaces and the decay of weak solutions in some anisotropic spaces for appropriate initial data.展开更多
In this paper we study the strong and weak property of travelling wave front solutions for a class of degenerate parabolic equations. How the strong and weak property changes under the effects of wave speed and reacti...In this paper we study the strong and weak property of travelling wave front solutions for a class of degenerate parabolic equations. How the strong and weak property changes under the effects of wave speed and reaction diffusion terms are showed.展开更多
In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also...In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also discussed.展开更多
This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotrop...This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.展开更多
In this paper we discuss the quasilinear parabolic equation Ut=△↓(u^α(1-u)^β.△↓u)+B(x,t,u)△↓u+C(x,t,u)which is degenerate at u=0 and u=1.Let u(x,t)be a weak solution of the equation satisfying 0<u(x,t)<1...In this paper we discuss the quasilinear parabolic equation Ut=△↓(u^α(1-u)^β.△↓u)+B(x,t,u)△↓u+C(x,t,u)which is degenerate at u=0 and u=1.Let u(x,t)be a weak solution of the equation satisfying 0<u(x,t)<1.Under some assumptions we establish Hoelder continuity of u(x,t).展开更多
目的研究TWEAK和Fn14在腰椎间盘退变髓核组织中的表达及其临床意义。方法用半定量RT-PCR和免疫组织化学法检测实验组(30例退变腰椎间盘)和对照组(10例创伤腰椎间盘)中TWEAK和Fn14 mRNA及蛋白表达。结果实验组TWEAK mRNA表达显著高于对照...目的研究TWEAK和Fn14在腰椎间盘退变髓核组织中的表达及其临床意义。方法用半定量RT-PCR和免疫组织化学法检测实验组(30例退变腰椎间盘)和对照组(10例创伤腰椎间盘)中TWEAK和Fn14 mRNA及蛋白表达。结果实验组TWEAK mRNA表达显著高于对照组(0.949±0.093 vs 0.653±0.110,P<0.01),实验组TWEAK蛋白表达显著高于对照组(0.682±0.126 vs 0.397±0.057,P<0.01),实验组Fn14 mRNA表达显著高于对照组(0.936±0.125 vs 0.632±0.059,P<0.01),Fn14蛋白表达显著高于对照组(0.540±0.051 vs 0.344±0.072,P<0.01)。结论 TWEAK和Fn14的表达增加可能参与腰椎间盘退变的进程。展开更多
The aim of this paper is to discuss the Cauchy problem for quasilinear degenerate parabolic equations of the formwhere φ∈C1(R1) is a strictly monotonically increasing function. Clearly, the above equation has strong...The aim of this paper is to discuss the Cauchy problem for quasilinear degenerate parabolic equations of the formwhere φ∈C1(R1) is a strictly monotonically increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of φ'(-) is permitted to have zero measure. In particular, the existence of interfaces of solutions is obtained.展开更多
Let Q（x） be a nonnegative definite, symmetric matrix such that √Q（X） is Lipschitz con- tinuous. Given a real-valued function b（x） and a weak solution u（x） of div（QVu） = b, we find sufficient conditions in o...Let Q（x） be a nonnegative definite, symmetric matrix such that √Q（X） is Lipschitz con- tinuous. Given a real-valued function b（x） and a weak solution u（x） of div（QVu） = b, we find sufficient conditions in order that √Qu has some first order smoothness. Specifically, if is a bounded open set in Rn, we study when the components of vVu belong to the first order Sobolev space W1＇2（Ω） defined by Sawyer and Wheeden. Alternately we study when each of n first order Lipschitz vector field derivatives Xiu has some first order smoothness if u is a weak solution in Ω of ^-^-1 X^Xiu ＋ b = O. We do not assume that {Xi}is a HSrmander collection of vector fields in ~. The results signal ones for more general equations.展开更多
文摘We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
基金Research supported by NSFC (10471149)Special Fund of Mathematics Research of Natural Science Foundation of Hebei Province (07M003)Doctoral Foundation of Hebei Province Ministry of Education (B2004103).
文摘The authors first give the definition of degenerate weakly （K1,K2）-quasiregular mappings using the technique of exterior power and exterior differential forms, and then, using the method of McShane extension, a useful inequality is obtained, which can be used to derive the self-improving regularity.
文摘In this paper,we consider solving numerically for the first time inverse problems of determining the time-dependent thermal diffusivity coefficient for a weakly degenerate heat equation,which vanishes at the initial moment of time,and/or the convection coefficient along with the temperature for a one-dimensional parabolic equation,from some additional information about the process(the so-called over-determination conditions).Although uniquely solvable these inverse problems are still ill-posed since small changes in the input data can result in enormous changes in the output solution.The finite difference method with the Crank-Nicolson scheme combined with the nonlinear Tikhonov regularization are employed.The resulting minimization problem is computationally solved using the MATLAB toolbox routine lsqnonlin.For both exact and noisy input data,accurate and stable numerical results are obtained.
文摘It is obtained the existence of the weak solution for a degenerate generalized Burgers equation under the restriction u0 ∈ L∞. The main method is to add viscosity perturbation and obtain some estimates in L1 norm. Meanwhile it is obtained the solution is exponential decay when the initial data has compact support.
文摘In this paper, the authors consider a system of degenerate Davey-Stewartson equations. They prove the global existence of weak solutions in some weighted function spaces and the decay of weak solutions in some anisotropic spaces for appropriate initial data.
文摘In this paper we study the strong and weak property of travelling wave front solutions for a class of degenerate parabolic equations. How the strong and weak property changes under the effects of wave speed and reaction diffusion terms are showed.
基金Supported by National Natural Science Foundation of China(10171113 and 10471156)Natural Science Foundation of GuangDong 2004(4009793).
文摘In this article, a degenerate and singular diffusion problem is studied. The existence of solutions is established by parabolic regularization. Some properties of solutions, for instance, asymptotic behavior, are also discussed.
基金The project is supported by NNSF of China (10371116)
文摘This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.
文摘In this paper we discuss the quasilinear parabolic equation Ut=△↓(u^α(1-u)^β.△↓u)+B(x,t,u)△↓u+C(x,t,u)which is degenerate at u=0 and u=1.Let u(x,t)be a weak solution of the equation satisfying 0<u(x,t)<1.Under some assumptions we establish Hoelder continuity of u(x,t).
文摘目的研究TWEAK和Fn14在腰椎间盘退变髓核组织中的表达及其临床意义。方法用半定量RT-PCR和免疫组织化学法检测实验组(30例退变腰椎间盘)和对照组(10例创伤腰椎间盘)中TWEAK和Fn14 mRNA及蛋白表达。结果实验组TWEAK mRNA表达显著高于对照组(0.949±0.093 vs 0.653±0.110,P<0.01),实验组TWEAK蛋白表达显著高于对照组(0.682±0.126 vs 0.397±0.057,P<0.01),实验组Fn14 mRNA表达显著高于对照组(0.936±0.125 vs 0.632±0.059,P<0.01),Fn14蛋白表达显著高于对照组(0.540±0.051 vs 0.344±0.072,P<0.01)。结论 TWEAK和Fn14的表达增加可能参与腰椎间盘退变的进程。
基金Project supported by the Teaching and Research Award Found for Outstanding Young Teachers in Higher Education Institutions of MOE ([2000]26)China and the NNSF (1001015) of China
文摘The aim of this paper is to discuss the Cauchy problem for quasilinear degenerate parabolic equations of the formwhere φ∈C1(R1) is a strictly monotonically increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of φ'(-) is permitted to have zero measure. In particular, the existence of interfaces of solutions is obtained.
文摘Let Q（x） be a nonnegative definite, symmetric matrix such that √Q（X） is Lipschitz con- tinuous. Given a real-valued function b（x） and a weak solution u（x） of div（QVu） = b, we find sufficient conditions in order that √Qu has some first order smoothness. Specifically, if is a bounded open set in Rn, we study when the components of vVu belong to the first order Sobolev space W1＇2（Ω） defined by Sawyer and Wheeden. Alternately we study when each of n first order Lipschitz vector field derivatives Xiu has some first order smoothness if u is a weak solution in Ω of ^-^-1 X^Xiu ＋ b = O. We do not assume that {Xi}is a HSrmander collection of vector fields in ~. The results signal ones for more general equations.
