Heat conduction in anisotropic media: Nonlinear self-adjointness and conservation laws

TL;DR

This paper investigates the nonlinear self-adjointness of anisotropic heat equations with sources, identifying models that admit conservation laws based on their symmetries, thus advancing understanding of heat conduction in complex media.

Contribution

It introduces a class of self-adjoint models for anisotropic nonlinear heat equations and computes associated conservation laws based on their symmetries.

Findings

Identified a class of self-adjoint models for anisotropic heat equations.

Derived conservation laws corresponding to symmetries of these models.

Enhanced understanding of heat conduction in anisotropic media with sources.

Abstract

Nonlinear self-adjointness of the anisotropic nonlinear heat equation is investigated. Mathematical models of heat conduction in anisotropic media with a source are considered and a class of self-adjoint models is identified. Conservation laws corresponding to the symmetries of the equations in question are computed.