An Inverse Problem for a Phase-field Model in Sobolev Spaces

Abstract

We prove an existence and uniqueness result for an inverse problem arising from a phase-field model with two memory kernels. More precisely, we identify the convolution memory kernels and the diffusion coefficient besides the temperature and the phase-field parameter. We prove our results in the framework of Sobolev spaces. Our fundamental tools are an optimal regularity result in the Lp spaces and fixed point arguments.KeywordsPhase-field system with memoryheat equationCahn-Hilliard type equationinverse problemoptimal regularity in Lp