带记忆项的反应扩散方程适定性问题
Well-Posed Problem for Reaction Diffusion Equation with Memory
摘要: 本文主要讨论带有记忆项的反应扩散方程适定性问题。利用Galerkin方法、能量估计以及紧性定理对空间H10(Ω)×L2μ(R+,H10(Ω)∩H2(Ω))中整体强解的适定性进行了研究，获得在非线性项满足任意阶指数增长条件下，系统整体强解的存在唯一性及连续性。
Abstract: The problem of the suitability of the reaction diffusion equation with memory terms is discussed in this paper. Using Galerkin method, energy estimation and compactness theorem, this paper studies the well-posed of the overall strong solution in space H10(Ω)×L2μ(R+,H10(Ω)∩H2(Ω)). The existence, uniqueness and continuous dependence are obtained under the condition that nonlinear terms satisfy the exponential growth of any order.
文章引用：张江卫, 罗双利, 李军. 带记忆项的反应扩散方程适定性问题[J]. 应用数学进展, 2018, 7(11): 1418-1428. https://doi.org/10.12677/AAM.2018.711166

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