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.
In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-di...In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary.展开更多
The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p...The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the L p entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.展开更多
In this paper,we study a free boundary problem of tumor growth with necrotic core.The model is a parabolic-hyperbolic partial differential equations,which is composed of three first-order nonlinear hyperbolic equation...In this paper,we study a free boundary problem of tumor growth with necrotic core.The model is a parabolic-hyperbolic partial differential equations,which is composed of three first-order nonlinear hyperbolic equations,a parabolic equation and an ordinary differential equation.First,we obtained the approximation model by polishing the Heaviside function,and then proved the existence and uniqueness of the solution of the approximation model.In addition,we improved the regularity of solution of the approximate problem by using the characteristic curves method,and finally proved the global existence of the weak solution of the original problem by the convergence.展开更多
In this article, we prove a general existence theorem for a class of nonlinear degenerate parabolichyperbolic equations. Since the regions of parabolicity and hyperbolicity are coupled in a way that depends on the sol...In this article, we prove a general existence theorem for a class of nonlinear degenerate parabolichyperbolic equations. Since the regions of parabolicity and hyperbolicity are coupled in a way that depends on the solution itself, there is almost no hope of decoupling the regions and then taking into account the parabolic and the hyperbolic features separately. The existence of solutions can be obtained by ?nding the limit of solutions for the regularized equation of strictly parabolic type. We use the energy methods and vanishing viscosity methods to prove the local existence and uniqueness of solution.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Supported by the National Natural Science Foundation of China(11131005)the Fundamental Research Funds for the Central Universities(2014201020202)
文摘In this paper, we use contraction mapping principle, operator-theoretic approach and some uniform estimates to establish local solvability of the parabolic-hyperbolic type chemotaxis system with fixed boundary in 1-dimensional domain. In addition, local solvability of the free boundary problem is considered by straightening the free boundary.
基金Yachun Li’s research was supported partly by National Natural Science Foundation of China (10571120,10971135)the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546)+3 种基金Shanghai Shuguang Project 06SG11Zhigang Wang’s research was supported partly by Shanghai Jiao Tong University Innovation Fund For Postgraduates (AE071202)the University Young Teacher Sciences Foundation of Anhui Province (2010SQRL145)the Quality Project Found of Fuyang Normal College (2010JPKC07)
文摘The aim of this paper is to prove the well-posedness（existence and uniqueness） of the L p entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with L p initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the L p entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.
基金supported the Characteristic Innovation Projects of Higher Learning in Guangdong Province(No.2016KTSCX028)the High-Level Talents Project of Guangdong Province(No.2014011).
文摘In this paper,we study a free boundary problem of tumor growth with necrotic core.The model is a parabolic-hyperbolic partial differential equations,which is composed of three first-order nonlinear hyperbolic equations,a parabolic equation and an ordinary differential equation.First,we obtained the approximation model by polishing the Heaviside function,and then proved the existence and uniqueness of the solution of the approximation model.In addition,we improved the regularity of solution of the approximate problem by using the characteristic curves method,and finally proved the global existence of the weak solution of the original problem by the convergence.
基金supported by National Natural Science Foundation of China (Grant Nos. 11631011 and 11626251)
文摘In this article, we prove a general existence theorem for a class of nonlinear degenerate parabolichyperbolic equations. Since the regions of parabolicity and hyperbolicity are coupled in a way that depends on the solution itself, there is almost no hope of decoupling the regions and then taking into account the parabolic and the hyperbolic features separately. The existence of solutions can be obtained by ?nding the limit of solutions for the regularized equation of strictly parabolic type. We use the energy methods and vanishing viscosity methods to prove the local existence and uniqueness of solution.
