非局部抛物问题的惯性流形
Inertial manifolds for the nonlocal parabolic problem
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中文总结 AI 辅助
本文针对一类非局部抛物问题，提出研究其惯性流形的抽象框架，通过调整非局部项得到谱间隙条件，成功证明了正方形域上二维非局部反应扩散方程的惯性流形存在性。
中文摘要 AI 辅助
本文为研究一类非局部抛物问题对应的惯性流形提供了抽象框架，通过适当地修改吸收球外的非局部项推导了相应的谱间隙条件；作为应用，我们在正方形域上的二维非局部反应扩散方程中建立了惯性流形的存在性。
英文摘要
This paper provides an abstract framework for studying inertial manifolds associated with a class of nonlocal parabolic problems. In particular, by suitably modifying the nonlocal term outside the absorbing ball and changing the scale of time, we derive a corresponding spectral gap condition. As applications, we establish the existence of inertial manifolds for two classes of two-dimensional modified nonlocal parabolic equations on a square domain, whose diffusion coefficients depend on the $L^2$-norm of the solution and of its gradient, respectively.
