Existence, uniqueness and asymptotic behavior of solutions for a nonclassical diffusion equation with delay
Existence, uniqueness and asymptotic behavior of solutions for a nonclassical diffusion equation with delay
复制标题
DOI：
10.4310/dpde.2013.v10.n3.a3
复制
发表时间：
2013
影响因子：
1.3
通讯作者：
T. Caraballo;A. M. Márquez-Durán
中科院分区：
文献类型：
--
作者：
T. Caraballo;A. M. Márquez-Durán
分析了一类具有时滞的非经典非自治扩散方程。首先，利用伽辽金近似和能量法证明了解的存在唯一性。其次，我们证明了平稳解的存在性和最终唯一性，以及它们的指数稳定性。我们强调，对延迟项施加的假设特别包括可测量变量延迟的情况。
A nonclassical nonautonomous diffusion equation with delay is analyzed. First, we prove the existence and uniqueness of solutions by using the Galerkin approximations and the energy method. Next, we prove the existence and eventual uniqueness of stationary solutions, as well as their exponential stability. We emphasize that the assumptions imposed on the delay term include, in particular, the case of measurable variable delays.