Our goal is to establish some sufficient conditions for the solvability of the nonlocal final value problem involving a class of partial differential equations, which describes the anomalous diffusion phenomenon. Our analysis is based on the theory of completely positive functions, resolvent operators and fixed point arguments in suitable function spaces. Especially, utilizing the regularity of resolvent operators, we are able to deal with non-Lipschitz cases. The obtained results, in particular, extend recent ones proved for fractional diffusion equations.

中文翻译：

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半线性反常扩散方程控制的非局部最终值问题

我们的目标是为涉及一类偏微分方程的非局部最终值问题的可求解性建立一些充分的条件，该条件描述了异常扩散现象。我们的分析基于完全正函数，可分解算子和适当函数空间中的不动点参数的理论。尤其是，利用解析操作符的规则性，我们能够处理非Lipschitz案例。所得结果尤其扩展了分数扩散方程证明的最新结果。