Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source

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作者：
Andrea N Ceretani
Domingo A Tarzia
Luis T Villa
机构：
[1] Universidad Austral,CONICET
[2] Universidad Nacional de Salta, Departamento de Matemática, Facultad de Ciencias Empresariales
来源：
Boundary Value Problems | / 2015卷
关键词：
non-classical heat equation; nonlinear heat conduction problems; explicit solutions; Volterra integral equations; 35C05; 35C15; 35C20; 35K55; 45D05; 80A20;
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摘要：
A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition is studied. It is not a standard heat conduction problem because a non-uniform heat source dependent on the heat flux at the boundary is considered. The purpose of this article is to find explicit solutions and analyze how to control their asymptotic temporal behavior through the source term.
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