A Note on Doubly Nonlinear Parabolic Systems with Unilateral Constraint

TL;DR

This paper establishes the existence and uniqueness of solutions for doubly nonlinear parabolic systems with unilateral constraints, using variational inequalities, penalty methods, and Gronwall's technique.

Contribution

It introduces a novel approach to handle unilateral constraints in doubly nonlinear parabolic systems through variational inequalities and analytical techniques.

Findings

Proved existence of solutions under given conditions.

Established uniqueness of solutions.

Applied penalty method and Gronwall's inequality successfully.

Abstract

We prove the existence and uniqueness of the solution to the doubly nonlinear parabolic systems with mixed boundary conditions. Due to the unilateral constraint the problem comes as a variational inequality. We apply the penalty method and Gronwall's technique to prove the existence and uniqueness of the variational solution.