On existence and uniqueness of solutions of thermal phase field models with a general class of nonlinearities

TL;DR

This paper establishes the existence and uniqueness of solutions for a broad class of nonlinear thermal phase field models, extending previous results to more general nonlinearities and temperature variations.

Contribution

It generalizes existing theoretical results by proving existence and uniqueness for a wider class of nonlinear parabolic systems in thermal phase field modeling.

Findings

Proved existence of solutions for generalized nonlinear phase field models.

Established uniqueness of solutions under broad conditions.

Extended previous models to include temperature variations and complex nonlinearities.

Abstract

We prove the existence and uniqueness of solutions for a family of nonlinear parabolic systems related to phase field models taking in account variations of temperature and the possibility of a general class of nonlinearities. The present results generalizes in certain aspects the already published ones in the literature.