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

N. SALVA D.A. TARZIA L.T. VILLA

BOUNDARY VALUE PROBLEMS

HINDAWI PUBLISHING CORPORATION

Lugar: New York; Año: 2011 vol. 2011 p. 1 - 17

1687-2762

A nonlinear problem for the one-dimensional heat equation in a bounded and homogeneous medium with temperature data on the boundary x=0 and x=1 is studied. It is considered a non-classical heat conduction problem because a uniform spatial heat source depending on the heat flux (or the temperature) on the boundary x=0 is taken into account. Existence and uniqueness for the solution are proved under suitable assumptions on the data. Comparisons results and asymptotic behavior for the solution for particular choices of the heat source, initial, and boundary data are also obtained. We also consider a generalization for non-classical moving boundary problems for the heat equation.