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Nonlinear hyperbolic-parabolic system Modeling Some Biological Phenomena

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Journal of Partial Differential Equations 2011年第1期24卷 1-14页

作者： WU Shaohua CHEN Hua School of Mathematics and Statistics Wuhan University Wuhan 430072 China.

In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N = 1, the global existence of the weak solution will be established by the bootstrap argument.

关键词： hyperbolic-parabolic system chemosensitive movement external signal global existence.

Global analysis of smooth solutions to a hyperbolic-parabolic coupled system

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Frontiers of Mathematics in China 2013年第6期8卷 1437-1460页

作者： Yinghui ZHANG Haiying DENG Mingbao SUN Department of Mathematics Hunan Institute of Science and Technology Yueyang 414006 China School of Mathematics and Statistics Central China Normal University Wuhan 430079 China Department of Mathematics Hunan First Normal College Changsha 410205 China

We investigate a model arising from biology, which is a hyperbolic- parabolic coupled system. First, we prove the global existence and asymptotic behavior of smooth solutions to the Cauchy problem without any smallness assumption on the initial data. Second, if the Hs ∩ Ll-norm of initial data is sufficiently small, we also establish decay rates of the global smooth solutions. In particular, the optimal L2 decay rate of the solution and the almost optimal L2 decay rate of the first-order derivatives of the solution are obtained. These results are obtained by constructing a new nonnegative convex entropy and combining spectral analysis with energy methods.

关键词： Global analysis hyperbolic-parabolic system decay rate convex entropy

hyperbolic-parabolic CHEMOTAXIS system WITH NONLINEAR PRODUCT TERMS

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Journal of Partial Differential Equations 2008年第1期21卷 45-58页

作者： Chen Hua Wu Shaohua School of Mathematics and Statistics Wuhan University Wuhan 430072 China

We prove the local existence and uniqueness of week solution of the hyperbolic-parabolic Chemotaxis system with some nonlinear product terms. For one dimensional case, we prove also the global existence and uniqueness... 详细信息

关键词： hyperbolic-parabolic system Chemotaxis external signal.

GLOBAL EXISTENCE,UNIQUENESS,AND STABILITY FOR A NONLINEAR hyperbolic-parabolic PROBLEM IN PULSE COMBUSTION

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Acta Mathematica Scientia 2012年第1期32卷 41-74页

作者： Olga Terlyga Hamid Bellout Frederick Bloom Fermi National Laboratory Department of Mathematical Sciences Northern Illinois University

A global existence theorem is established for an initial-boundary value prob- lem, with time-dependent boundary data, arising in a lumped parameter model of pulse combustion; the model in question gives rise to a nonlinear mixed hyperbolic-parabolic sys- tem. Using results previously established for the associated linear problem, a fixed point argument is employed to prove local existence for a regularized version of the nonlinear problem with artificial viscosity. Appropriate a-priori estimates are then derived which imply that the local existence result can be extended to a global existence theorem for the regularized problem. Finally, a different set of a priori estimates is generated which allows for taking the limit as the artificial viscosity parameter converges to zero; the corresponding solution of the regularized problem is then proven to converge to the unique solution of the initial-boundary value problem for the original, nonlinear, hyperbolic-parabolic system.

关键词： pulse combustion hyperbolic-parabolic system global existence regularity

On Existence of Local Solutions for a hyperbolic system Modelling Chemotaxis with Memory Term

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Journal of Partial Differential Equations 2021年第2期34卷 170-185页

作者： WU Shaohua WANG Pengfei School of Mathematics and Statistics Wuhan UniversityWuhan 430072China

In this paper,we discuss the-local existence of weak solutions for some hyperbolic parabolic systems modelling chemotaxis with memory *** main methods we use are the fixed point theorem and semigroup theory.

关键词： hyperbolic-parabolic system KS model chemotaxis memory term