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Initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal boundary condition*

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Abstract

We consider an initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal Neumann boundary condition. We prove a comparison principle and the existence of a local solution and study the problem of uniqueness and nonuniqueness.

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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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∗This work is supported by the state program of fundamental research of Belarus, grant 1.2.03.1.

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Gladkov, A. Initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal boundary condition* . Lith Math J 57, 468–478 (2017). https://doi.org/10.1007/s10986-017-9376-x

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  • DOI: https://doi.org/10.1007/s10986-017-9376-x

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