Existence and uniqueness of the solution of a space–time periodic reaction–diffusion equation
Existence and uniqueness of the solution of a space–time periodic reaction–diffusion equation
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DOI：
10.1016/j.jde.2010.05.007
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发表时间：
2010-09
影响因子：
2.4
通讯作者：
Grégoire Nadin
中科院分区：
文献类型：
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作者：
Grégoire Nadin
本文研究了方程的周期解和整体解：其中扩散矩阵A，对流项q和反应项f在t和x上都是周期的。我们证明了线性化问题的周期主特征值的符号决定了周期解的存在性和唯一性。引入另一个特征值，我们能够状态的唯一性条件，整个解决方案，并得出相关的柯西问题的解决方案的渐近行为。
This paper is concerned with the study of the periodic solutions and the entire solutions of the equation: where the diffusion matrix A, the advection term q and the reaction term f are periodic in t and x. We prove that the sign of the periodic principal eigenvalue associated with the linearized problem determines the existence and the uniqueness of the periodic solution. Introducing another eigenvalue, we are able to state uniqueness conditions for the entire solution and to derive the asymptotic behavior of the solutions of the associated Cauchy problem.