带记忆项发展方程在ℝⁿ上的适定性

Well-Posed for Evolution Equations with Memory Term on ℝⁿ

在本文中,主要研究带记忆项反应扩散方程在无界域上的适定性问题,应用经典的Galerkin方法得到了整体弱解的存在性,同时证明了解的唯一性和解对初值的连续依赖性,其中非线性项满足任意阶指数增长。

In this paper, we mainly study the suitability of the reaction-diffusion equation with memory term in the unbounded domain, obtain the existence of the global weak solution by classical Galerkin method, and prove the uniqueness of the understanding and the continuous dependence on the initial value, where the nonlinear term satisfies the exponential growth of any order.