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Global existence and blow-up of solutions of nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition

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Abstract

In this paper we consider initial boundary value problem for nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition and nonnegative initial datum. We prove comparison principle, global existence and blow-up of solutions.

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Acknowledgements

This work is supported by the state program of fundamental research of Belarus (grant 1.2.03.1). The author is also thankful to an anonymous referee whose remarks have improved the paper.

Funding

Belarusian Republican Foundation for Fundamental Research, Grant no. 1.2.02.2.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Belarusian State University, Nezavisimosti Avenue 4, 220030, Minsk, Belarus

    Alexander Gladkov

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  1. Alexander Gladkov
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Correspondence to Alexander Gladkov.

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Communicated by Joachim Escher.

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Gladkov, A. Global existence and blow-up of solutions of nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition. Monatsh Math 203, 357–372 (2024). https://doi.org/10.1007/s00605-023-01892-5

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