Asymptotic behavior of solutions to a wave equation with a nonlinear dissipative term in \(\mathbb R^n\). (English) Zbl 1098.35028
The paper deals with the initial value problem to the equation \(u_{tt}-\triangle u+g(u_{t})=0\) in \(\mathbb R^n\times \mathbb R_+.\) Under some restrictions on the dissipation function \(g\) and initial data the author proves the asymptotic energy estimate of a solution to the problem for \(t\rightarrow \infty\).
Reviewer: Marie Kopáčková (Praha)
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B37 | PDE in connection with control problems (MSC2000) |
| 35L70 | Second-order nonlinear hyperbolic equations |
| 35L15 | Initial value problems for second-order hyperbolic equations |
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