Abstract
In this paper, we investigate asymptotic behavior for the solution of the Petrovsky equation with locally distributed damping. Without growth condition on the damping at the origin, we extend the energy decay result in Martinez (Rev. Math. Complut. Madr. 12(1):251–283, 1999) for the single wave equation to the Petrovsky equation. The explicit energy decay rate is established by using piecewise multiplier techniques and weighted nonlinear integral inequalities.
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This work was supported by the National Natural Science Foundation of China 10771032, the Natural Science Foundation of Jiangsu province BK2006088 and JSPS Innovation Program CX08B_001Z.
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Han, X., Wang, M. Asymptotic Behavior for Petrovsky Equation with Localized Damping. Acta Appl Math 110, 1057–1076 (2010). https://doi.org/10.1007/s10440-009-9493-6
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DOI: https://doi.org/10.1007/s10440-009-9493-6