Existence and uniqueness of mild solutions for a final value problem for nonlinear fractional diffusion systems

Authors: Tran Bao Ngoc, Donal O'Regan, Nguyễn Huy Tuấn, Nguyễn Huy Tuấn, Donal O’Regan,

https://doi.org/10.1016/j.cnsns.2019.104882

Publisher, magazine: ,

Publication year: 2019

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Abstract

We consider a Cauchy semilinear problem for a time-fractional diffusion system which involves symmetric uniformly elliptic operators on a bounded domain Ω in with sufficiently smooth boundary. The problem is equipped with final value conditions (FVCs), i.e., are given. We derive a spectral representation of solutions with FVCs where the solution operators are not bounded on L2(Ω). Our work focuses on establishing existence and uniqueness of a solution in a suitable space.

Tags: Final value problem, Fractional diffusion system, Fixed point theory