Optimal decay rates for solutions of a nonlinear wave equation with localized nonlinear dissipation of unrestricted growth and critical exponent source terms under mixed boundary conditions |
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Authors: | Daniel Toundykov |
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Institution: | Department of Mathematics, University of Virginia, 22904 Charlottesville, VA, United States |
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Abstract: | This article investigates optimal decay rates for solutions to a semilinear hyperbolic equation with localized interior damping and a source term. Both dissipation and the source are fully nonlinear and the growth rate of the source map may include critical exponents (for Sobolev’s embedding H1→L2). Besides continuity and monotonicity, no growth or regularity assumptions are imposed on the damping. We analyze the system in the presence of Neumann-type boundary conditions including the mixed cases: Dirichlet–Neumann–Robin. |
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Keywords: | 35L20 35L70 93D20 |
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