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Uniform stabilization of solution. (English) Zbl 0977.35025
The author proves the exponential decay of solution of the initial-boundary value problem to the equation \(u_{tt}-(\alpha +2\beta \|\nabla u\|_2^2)\triangle u+\delta u=\mu u^3\), \(x\in \Omega \), \(t>0\), satisfying the homogeneous Dirichlet condition on the boundary of \(\Omega \).
MSC:
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
35L70 Second-order nonlinear hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
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