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Blow up in a semilinear pseudo-parabolic equation with variable exponents

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Abstract

In this paper, we consider the following pseudo-parabolic equation with variable exponents:

$$\begin{aligned} u_{t}-\Delta u-\Delta u_{t}+\int _{0}^{t}g(t-\tau )\Delta u(x,\tau )d \tau = |u|^{p(x)-2}u. \end{aligned}$$

Under suitable assumptions on the initial datium \(u_{0}\), the relaxation function g and the variable exponents p, we prove that any weak solution, with initial data at arbitrary energy level, blows up in finite time.

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Acknowledgements

The authors thank University of Sharjah and Birzeit University for their support. This work was partially supported by MASEP Research Group in the Research Institute of Sciences and Engineering at University of Sharjah.

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Authors and Affiliations

  1. Department of Mathematics, University of Sharjah, P.O. Box 27272, Sharjah, UAE

    Salim A. Messaoudi

  2. Department of Mathematics, Birzeit University, West Bank, Palestine

    Ala A. Talahmeh

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  1. Salim A. Messaoudi
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  2. Ala A. Talahmeh
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Correspondence to Salim A. Messaoudi.

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Messaoudi, S.A., Talahmeh, A.A. Blow up in a semilinear pseudo-parabolic equation with variable exponents. Ann Univ Ferrara 65, 311–326 (2019). https://doi.org/10.1007/s11565-019-00326-1

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  • DOI: https://doi.org/10.1007/s11565-019-00326-1

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