Type of Publication:  Journal article 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:352opus96367 
Author:  Muñoz Rivera, Jaime E.; Racke, Reinhard 
Year of publication:  2008 
Published in:  Nonlinear Analysis : theory, methods & applications ; 68 (2008), 9.  pp. 25312551.  ISSN 0362546X.  eISSN 18735215 
DOI (citable link):  https://dx.doi.org/10.1016/j.na.2007.02.022 
Summary: 
We consider the nonlinear wave equation utt−σ(ux)x+a(x)ut=0 in a bounded interval (0, L) C R1. The function a is allowed to change sign, but has to satisfy a = 1/LR L 0 a(x)dx > 0. For this nondissipative situation we prove the exponential stability of the corresponding linearized system for: (I) possibly large aL∞ with small a(·) − aL2, and (II) a class of pairs (a,L) with possibly negative moment R L0 a(x) sin2(pi x/L) dx. Estimates for the decay rate are also given in terms of a. Moreover, we show the global existence of smooth, small solutions to the corresponding nonlinear system if, additionally, the negative part of a is small enough.

MSC Classification:  35B40; 35L70 
Subject (DDC):  510 Mathematics 
Keywords:  Indefinite damping, Wave equation, Exponential stability 
Link to License:  In Copyright 
Bibliography of Konstanz:  Yes 
MUÑOZ RIVERA, Jaime E., Reinhard RACKE, 2008. Exponential stability for wave equations with nondissipative damping. In: Nonlinear Analysis : theory, methods & applications. 68(9), pp. 25312551. ISSN 0362546X. eISSN 18735215. Available under: doi: 10.1016/j.na.2007.02.022
@article{MunozRivera2008Expon737, title={Exponential stability for wave equations with nondissipative damping}, year={2008}, doi={10.1016/j.na.2007.02.022}, number={9}, volume={68}, issn={0362546X}, journal={Nonlinear Analysis : theory, methods & applications}, pages={25312551}, author={Muñoz Rivera, Jaime E. and Racke, Reinhard} }
Exponential_stability_for_wave_equations_with_non_dissipative_damping.pdf  179 