Dynamics of Partial Differential Equations

Volume 19 (2022)

Number 3

Dual Lyapunov approach to finite time stability for parabolic PDE

Pages: 177 – 189

DOI: https://dx.doi.org/10.4310/DPDE.2022.v19.n3.a1

Authors

Anna Michalak (Faculty of Economics and Sociology, University of Lodz, Poland)

Andrzej Nowakowski (Faculty of Economics and Sociology, University of Lodz, Poland)

Abstract

We investigate stability and finite time stability properties of the zero solution to a semilinear parabolic equation. To this effect we develop a new, dual approach to Lyapunov concept of stability. The dual Lyapunov function satisfies a dual Hamilton–Jacobi inequality. This is a basis to study finite time stability (finite extinction time) of the original problem.

Keywords

stability, finite time stability, finite extinction time, dual Lyapunov stability, parabolic equation

2010 Mathematics Subject Classification

35B35

Received 28 September 2021

Published 23 May 2022