一类非线性反应扩散耦合系统的整体解和爆破
Global Solution and Blow-Up for a Class of Nonlinear Reaction Diffusion Coupled Systems
摘要:
本文研究一类带有扩散项的非线性抛物方程组的初边值问题，借助Sobolev嵌入定理，Gagliardo-Niren- berg不等式，利用Galerkin方法，建立了弱解整体存在和爆破的充分条件，结合伯努利不等式得到了弱解整体存在时的有界性。
Abstract:
In this paper, the initial boundary value problem for a class of Nonlinear Parabolic Equations with diffusion term is studied. By means of Sobolev embedding theorem, Gagliardo Nirenberg inequality and Galerkin method, sufficient conditions for the global existence and blow up of weak solutions are established. The boundedness of global existence of weak solutions is obtained by combining Bernoulli inequality.
参考文献
|
[1]
|
Raposo, C.A., et al. (2008) Solution and Asymptotic Behaviour for a Nonlocal Coupled System of Reaction-Diffusion. Acta Applicandae Mathematicae, 102, 37-56. [Google Scholar] [CrossRef]
|
|
[2]
|
Rui, M.P. (2016) A Reaction-Diffusion Model for the Non-Local Coupled System: Existence, Uniqueness, Long-Time Behaviour and Localization Properties of Solutions. IMA Journal Applied Mathematics, 81, 344-364. [Google Scholar] [CrossRef]
|
|
[3]
|
Tsutsumi, M. (1972) Existence and Nonexistence of Global Solutions for Nonlinear Parabolic Equations. Publicational of the Research Institute for Mathematical Sciences, 8, 211-229. [Google Scholar] [CrossRef]
|
|
[4]
|
Ladyzhenskaya, O.A., Solonnikov, V.A. and Uralceva, N.N. (1968) Linear and Quasi-Linear Equations of Parabolic Type. American Mathematical Society. [Google Scholar] [CrossRef]
|
|
[5]
|
葛健芽. Bernoulli不等式的几个标记[J]. 浙江师范大学学报(自然科学版), 2003, 26(2): 119-122.
|