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Existence of solutions for a class of heat equations involving the mean curvature operator

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Abstract

The goal of this paper is to show the existence of a bounded variation solution, which is based on the Anzellotti pairing to an evolution problem associated with the minimal surface equations. A key ingredient in the proof is to approximate the parabolic minimal surface problem by a quasilinear parabolic problem involving a parameter \(p>1\), and then by establishing some energy estimates independent of p, we take the limit as \(p\rightarrow 1^{+}\) to obtain the desired result.

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Authors and Affiliations

  1. Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, Campina Grande, PB, 58429-970, Brazil

    Claudianor O. Alves

  2. Department of Basic Teaching, Institute of Electrical and Electronic Engineering, University of Boumerdes, 35000, Boumerdes, Algeria

    Tahir Boudjeriou

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  1. Claudianor O. Alves
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CA and TB wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Tahir Boudjeriou.

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Alves, C.O., Boudjeriou, T. Existence of solutions for a class of heat equations involving the mean curvature operator. Anal.Math.Phys. 13, 13 (2023). https://doi.org/10.1007/s13324-022-00774-7

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  • DOI: https://doi.org/10.1007/s13324-022-00774-7

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