On the principle of linearized stability in interpolation spaces for quasilinear evolution equations

TL;DR

This paper proves the exponential stability of equilibria in quasilinear parabolic evolution equations within specific interpolation spaces, advancing understanding of stability in these complex systems.

Contribution

It provides a rigorous proof of asymptotic exponential stability in interpolation spaces for quasilinear parabolic equations, a novel result in this area.

Findings

Exponential stability of equilibria established

Applicable to a broad class of quasilinear parabolic equations

Enhances theoretical understanding of stability in interpolation spaces

Abstract

We give a proof for the asymptotic exponential stability of equilibria of quasilinear parabolic evolution equations in admissible interpolation spaces.