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An application of semigroups of locally Lipschitz operators to Carrier equations with acoustic boundary conditions. (English) Zbl 1145.47044
Summary: A generation theorem for semigroups of locally Lipschitz operators on a subset of a real Banach space is given and applied to the problem of the well-posedness of the Carrier equation \(u_{tt} - \kappa (\| u\| ^{2})\Delta u+\gamma | u_t| ^{p - 1}u_t=0\) in \(\varOmega \times (0,\infty )\) with acoustic boundary condition, where \(p>2\) and \(\varOmega \) is a bounded domain in an arbitrary dimensional space.

MSC:
47H20 Semigroups of nonlinear operators
35L70 Second-order nonlinear hyperbolic equations
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