Publikation: Wave equations with non-dissipative damping
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2002
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Muñoz Rivera, Jaime E.
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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.
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510 Mathematik
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MUÑOZ RIVERA, Jaime E., Reinhard RACKE, 2002. Wave equations with non-dissipative dampingBibTex
@unpublished{MunozRivera2002equat-685, year={2002}, title={Wave equations with non-dissipative damping}, author={Muñoz Rivera, Jaime E. and Racke, Reinhard} }
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