Séminaire du MODMAD

Domingo Tarzia Depto. Matematica – CONICET, PARAGUAY

Speaker  :  Domingo Tarzia Depto. Matematica - CONICET, Paraguay

Title : Neumann solutions to fractional lamé-clapeyron-stefan problems with temperature, heat flux or convective boundary conditions

Abstract :
Generalized Neumann solutions for three two-phase fractional Lamé-Clapeyron-Stefan problems for a semi-infinite material are obtained with constant initial condition, and a boundary condition at the fixed face x=0 given by: a constant temperature, or a particular heat flux or a particular convective (Robin) condition.

In these problems, the two governing diffusion equations and a governing condition for the free boundary include a fractional time derivative in the Caputo sense of order 0<a<1. When a goes to 1 we recover the classical Neumann solutions for the two-phase Lamé-Clapeyron-Stefan problem through the error function, given in :

i)   Weber, Book (1901) for a temperature boundary condition;

ii)  T., Quart. Appl. Math. (1981) for a heat flux boundary condition when an inequality for the coefficient which characterizes the heat flux boundary condition is satisfied;

iii)   T., MAT - Serie A, 8 (2004) for a convective boundary condition when an inequality for the coefficient which characterizes the convective boundary condition is satisfied