Type of Publication:  Preprint 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:352opus21927 
Author:  Muñoz Rivera, Jaime E.; Racke, Reinhard 
Year of publication:  2002 
Series:  Konstanzer Schriften in Mathematik und Informatik ; 169 
Summary: 
We consider the nonlinear wave equation $u_{tt}\sigma(u_x)_x + a(x)u_t = 0$ in a bounded interval (0,L) subset IR1. The function a is allowed to change sign, but has to satisfy $\int \limits^L_0 a(x)dx > 0$ For this nondissipative situation we prove the exponential stability of the corresponding linearized system for small a, as well as the global existence of smooth, small solutions to the nonlinear system if in particular the negative part of a is small enough.

Subject (DDC):  510 Mathematics 
Link to License:  In Copyright 
MUÑOZ RIVERA, Jaime E., Reinhard RACKE, 2002. Wave equations with nondissipative damping
@unpublished{MunozRivera2002equat685, title={Wave equations with nondissipative damping}, year={2002}, author={Muñoz Rivera, Jaime E. and Racke, Reinhard} }
preprint_169.pdf  107 