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# Wave equations with non-dissipative damping

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MUÑOZ RIVERA, Jaime E., Reinhard RACKE, 2002. Wave equations with non-dissipative damping

@unpublished{MunozRivera2002equat-685, title={Wave equations with non-dissipative damping}, year={2002}, author={Muñoz Rivera, Jaime E. and Racke, Reinhard} }

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 non-dissipative 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. 2011-03-22T17:45:30Z 2011-03-22T17:45:30Z terms-of-use Racke, Reinhard Wave equations with non-dissipative damping 2002 Racke, Reinhard application/pdf Muñoz Rivera, Jaime E. Muñoz Rivera, Jaime E. eng

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