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Research Article | Open Access

Homogenization of the heat equation with random convolutional potential

Mengmeng Wang( ), Dong Su, Wei Wang
Department of Mathematics, Nanjing University, Nanjing 210093, China
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Abstract

This paper derived the homogenization of the heat equation with random convolutional potential. By Tartar's method of oscillating test function, the solution of the heat equation with random convolutional potential was shown to converge in distribution to the solution of the effective equation with determined convolutional potential.

Keywords

homogenizationweak convergencerandom convolutional potentialheat equation
CLC number: 35B27, 35K05, 60J45

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AIMS Mathematics
Volume 9 Issue 3,
March 2024
Pages 5661-5670
DOI: 10.3934/math.2024273

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Cite this article:
Wang M, Su D, Wang W. Homogenization of the heat equation with random convolutional potential. AIMS Mathematics, 2024, 9(3): 5661-5670. https://doi.org/10.3934/math.2024273

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Received: 16 October 2023
Revised: 28 December 2023
Accepted: 09 January 2024
Published: 15 March 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)