Global well-posedness for a time-fractional doubly nonlinear equation

TL;DR

This paper establishes the global existence and uniqueness of weak solutions for a complex time-fractional doubly nonlinear parabolic equation with maximal monotone nonlinearities and Lipschitz perturbations.

Contribution

It introduces a novel analysis for a time-fractional doubly nonlinear equation with maximal monotone graphs, extending existing theories to more general nonlinearities.

Findings

Proved existence of global weak solutions.

Established uniqueness under certain conditions.

Developed a regularization and Galerkin approximation approach.

Abstract

We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the growth. In addition, a Lipschitz continuous perturbation is considered. The existence of global weak solutions is obtained via a regularization and Galerkin approximation method. Uniqueness is also discussed under some additional assumptions.