On a nonlinear degenerate evolution equation with nonlinear boundary damping. (English) Zbl 1347.35176

Summary: This paper deals essentially with a nonlinear degenerate evolution equation of the form \(Ku''-\Delta u + \sum_{j = 1}^n b_j (\partial u' / \partial x_j) + | u|^\sigma u=0\) supplemented with nonlinear boundary conditions of Neumann type given by \(\partial u / \partial \nu + h(\cdot, u')=0\). Under suitable conditions the existence and uniqueness of solutions are shown and that the boundary damping produces a uniform global stability of the corresponding solutions.


35L80 Degenerate hyperbolic equations
35L71 Second-order semilinear hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
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