In this paper, we establish the global stability of the spatially nonhomogeneous steady state solution of a reaction diffusion equation with nonlocal delay under the Dirichlet boundary condition. To achieve this, we obtain the global existence and nonnegativity of solutions and give an extensive study on the properties of omega limit sets.

中文翻译：

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具有非局部延迟的反应-扩散方程的全局稳定性


在本文中，我们建立了在狄利克雷边界条件下具有非局部延迟的反应扩散方程的空间非均匀稳态解的全局稳定性。为了实现这一目标，我们获得了解的全局存在和非负性，并对 omega 极限集的性质进行了广泛的研究。