Stability results for doubly nonlinear differential inclusions by variational convergence

TL;DR

This paper establishes a stability framework for a broad class of doubly nonlinear differential inclusions using variational convergence, applicable even with nonconvex energies and in vanishing viscosity scenarios.

Contribution

It introduces a novel stability analysis method based on Fitzpatrick theory, extending the understanding of doubly nonlinear equations with complex energy functionals.

Findings

Stability results for doubly nonlinear equations with maximal monotone operators.

Applicability to vanishing viscosity approximations of rate-independent systems.

Framework accommodating nonconvex and nonsmooth energy functionals.

Abstract

We present a stability result for a wide class doubly nonlinear equations, featuring general maximal monotone operators, and (possibly) nonconvex and nonsmooth energy functionals. The limit analysis resides on the reformulation of the differential evolution as a scalar energy-conservation equation with the aid of the so-called Fitzpatrick theory for the representation of monotone operators. In particular, our result applies to the vanishing viscosity approximation of rate-independent systems.