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Existence theory and \(L^p\) estimates for the solution of nonlinear viscous wave equation. (English) Zbl 1202.35138

Summary: We consider the global existence of the Cauchy problem for the nonlinear viscous wave equation. We get the global existence theory directly by using the decaying properties of the solution. Such properties are obtained by long wave-short wave decomposition, Green’s function method and energy estimates. Finally, we show the \(L^p\) estimates for the solution by interpolation lemma.

MSC:

35L71 Second-order semilinear hyperbolic equations
35L15 Initial value problems for second-order hyperbolic equations
35A08 Fundamental solutions to PDEs
35B45 A priori estimates in context of PDEs
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