Strong solutions for semilinear wave equations with damping and source terms |
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Authors: | Petronela Radu |
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Institution: | 1. Department of Mathematics , University of Nebraska-Lincoln , 203 Avery Hall, Lincoln , NE 68588-0130 , USA pradu@math.unl.edu |
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Abstract: | This article deals with local existence of strong solutions for semilinear wave equations with power-like interior damping and source terms. A long-standing restriction on the range of exponents for the two nonlinearities governs the literature on wellposedness of weak solutions of finite energy. We show that this restriction may be eliminated for the existence of higher regularity solutions by employing natural methods that use the physics of the problem. This approach applies to the Cauchy problem posed on the entire ? n as well as for initial boundary problems with homogeneous Dirichlet boundary conditions. |
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Keywords: | wave equation local existence finite speed of propagation nonlinear damping interior source strong solutions |
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