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Existence and uniform decay of solutions of a parabolic-hyperbolic equation with nonlinear boundary damping and boundary source term. (English) Zbl 1022.35028

A mixed problem for a linear hyperbolic-parabolic equation is considered when on the part of the lateral boundary the Dirichlet condition is given and on the rest of the boundary a nonlinear damping and a source term are given. Under the assumption that the damping is predominant over the source, the existence of global solutions is proved. If the damping and the source terms have the same growth, the uniform decay of strong and weak solutions is proved.

MSC:

35M10 PDEs of mixed type
35B40 Asymptotic behavior of solutions to PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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