Nonlinear second order evolution inclusions with noncoercive viscosity term

TL;DR

This paper proves the existence of solutions for a second order nonlinear evolution inclusion with a noncoercive viscosity term using regularization and a priori bounds.

Contribution

It introduces a novel approach to handle noncoercive viscosity terms in second order evolution inclusions through regularization and limit processes.

Findings

Existence of solutions established for the nonlinear evolution inclusion.

Method handles nonmonotone, noncoercive viscosity terms effectively.

Provides a framework for similar nonlinear evolution problems.

Abstract

In this paper we deal with a second order nonlinear evolution inclusion, with a nonmonotone, noncoercive viscosity term. Using a parabolic regularization (approximation) of the problem and {\it a priori} bounds that permit passing to the limit, we prove that the problem has a solution.