On sharp decay estimates of solutions for mildly degenerate dissipative wave equations of Kirchhoff type. (English) Zbl 1222.35036
Summary: We consider the initial boundary value problem for degenerate dissipative wave equations of Kirchhoff type \(\rho u''+\|A^{1/2}u\|^{2\gamma} Au+ u'= 0\). When either the coefficient \(\rho \) or the initial data are appropriately small, we show global existence by using suitable identities. Moreover, under the same assumption for \(\rho \) and the initial data, we derive sharp decay estimates of the solutions and their second derivatives.
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35L71 | Second-order semilinear hyperbolic equations |
| 35R09 | Integro-partial differential equations |
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
Keywords:
energy decayReferences:
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