Exponential stability for wave equations with non-dissipative damping

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MUÑOZ RIVERA, Jaime E., Reinhard RACKE, 2008. Exponential stability for wave equations with non-dissipative damping. In: Nonlinear Analysis : theory, methods & applications. 68(9), pp. 2531-2551. ISSN 0362-546X. eISSN 1873-5215. Available under: doi: 10.1016/j.na.2007.02.022

@article{MunozRivera2008Expon-737, title={Exponential stability for wave equations with non-dissipative damping}, year={2008}, doi={10.1016/j.na.2007.02.022}, number={9}, volume={68}, issn={0362-546X}, journal={Nonlinear Analysis : theory, methods & applications}, pages={2531--2551}, author={Muñoz Rivera, Jaime E. and Racke, Reinhard} }

Muñoz Rivera, Jaime E. 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 non-dissipative situation we prove the exponential stability of the corresponding linearized system for: (I) possibly large ||a||L∞ with small ||a(·) − a||L2, 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. Exponential stability for wave equations with non-dissipative damping eng Racke, Reinhard 2008 application/pdf Muñoz Rivera, Jaime E. First publ. in: Nonlinear Analysis: Theory, Methods & Applications 68 (2008), 9, pp. 2531-2551 terms-of-use Racke, Reinhard 2011-03-22T17:45:40Z 2011-03-22T17:45:40Z

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