A new approach of strong stabilization of distributed systems
type: Item
instance of: scholarly article
title: A new approach of strong stabilization of distributed systems
zbMATH Open document ID: 1004.35092
published in: Differential and Integral Equations
publication date: 2000-05-29T00:00:00Z
review text: The author considers the Dirichlet initial-boundary value problem for the equation \(u'' - \Delta u + g(u') = 0\). His aim is to minimize the requirements guaranteeing the decay of energy solutions to zero for \(t \to +\infty \) by separating them from the assumptions ensuring the existence and uniqueness of solutions. Hence, his results weaken considerably usual assumptions and include functions \(g\) that are not monotone, have not polynomial growth near the origin and the domains of spatial variables \(\Omega \) of finite measure, not necessarily bounded. The author then extends the results to the above wave equation with additional terms either of the form \(f(u)\) or \(-\Delta u'\). The plate equation \(u'' + \Delta ^2 u - g(\Delta u') = 0\) is dealt with as well.
reviewed by: L. Herrmann
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 35L75
Mathematics Subject Classification ID: 35L35
zbMATH DE Number: 1453638
zbMATH Keywords: Dirichlet initial-boundary value problem
zbMATH Keywords: decay of energy
zbMATH Keywords: plate equation
author: Mohammed Aassila
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1453638