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On an evolution equation with acoustic boundary conditions. (English) Zbl 1230.35058
Summary: We analyze from the mathematical point of view a model for small vertical vibrations of an elastic string with weak internal damping and quadratic term, coupled with mixed boundary conditions of Dirichlet type and acoustic type. Our goal is to extend some of the results of C.L. Frota and J.A. Goldstein [J. Differ. Equations 164, No. 1, 92–109 (2000; Zbl 0979.35105)] in the sense of considering a weaker internal damping and one more quadratic nonlinearity in the elastic string equation.

MSC:
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L71 Second-order semilinear hyperbolic equations
35R09 Integral partial differential equations
74K05 Strings
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