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Lower and Upper Bounds for the Blow-Up Time of a Class of Damped Fourth-Order Nonlinear Evolution Equations

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Abstract

This paper is concerned with the study of the nonlinear damped wave equation

$$u_{tt}+{\Delta}^{2}u-{\Delta} u-\omega{\Delta} u_{t}+\alpha(t)u_{t}=\left\vert u\right\vert^{p-2}u, $$

in a bounded domain with smooth boundary. The blow-up of solutions are investigated under some conditions. Both lower and upper bounds for the blow-up time are derived when blow-up occurs.

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Acknowledgments

The author would like to thank the anonymous referee for his/her valuable and constructive suggestions which improve this work.

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Authors and Affiliations

  1. General Education Center, National Taipei University of Technology, Taipei, 106, Taiwan

    Shun-Tang Wu

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  1. Shun-Tang Wu
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Correspondence to Shun-Tang Wu.

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Wu, ST. Lower and Upper Bounds for the Blow-Up Time of a Class of Damped Fourth-Order Nonlinear Evolution Equations. J Dyn Control Syst 24, 287–295 (2018). https://doi.org/10.1007/s10883-017-9366-7

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  • DOI: https://doi.org/10.1007/s10883-017-9366-7

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