Open Access Research

An initial-boundary value problem for the one-dimensional non-classical heat equation in a slab

Natalia Nieves Salva12, Domingo Alberto Tarzia13* and Luis Tadeo Villa14

Author Affiliations

1 CONICET, Rosario, Argentina

2 TEMADI, Centro Atómico Bariloche, Av. Bustillo 9500, 8400 Bariloche, Argentina

3 Depto. de Matemática, Universidad Austral, Paraguay 1950, S2000FZF Rosario, Argentina

4 Facultad de Ingeniería, Universidad Nacional de Salta, Buenos Aires 144, 4400 Salta, Argentina

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Boundary Value Problems 2011, 2011:4  doi:10.1186/1687-2770-2011-4

Published: 29 June 2011

Abstract

Nonlinear problems for the one-dimensional heat equation in a bounded and homogeneous medium with temperature data on the boundaries x = 0 and x = 1, and a uniform spatial heat source depending on the heat flux (or the temperature) on the boundary x = 0 are studied. Existence and uniqueness for the solution to non-classical heat conduction problems, under suitable assumptions on the data, are obtained. Comparisons results and asymptotic behavior for the solution for particular choices of the heat source, initial, and boundary data are also obtained. A generalization for non-classical moving boundary problems for the heat equation is also given.

2000 AMS Subject Classification: 35C15, 35K55, 45D05, 80A20, 35R35.

Keywords:
Non-classical heat equation; Nonlinear heat conduction problems; Volterra integral equations; Moving boundary problems; Uniform heat source