A free boundary problem for a diffusion–convection equation. (April 2020)

• Record Type: Journal Article
• Authors: Briozzo, Adriana C.; Tarzia, Domingo A.
• Is Part Of: International journal of non-linear mechanics. Volume 120(2020)
• Publication Date: 2020-04
• Subjects: 35R35 -- 45D05 -- 35K55; Diffusion–convection equation -- Free boundary problem -- Nonlinear integral equation; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2019.103394
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: One-dimensional free boundary problem for a nonlinear diffusion–convection equation with a Dirichlet condition at fixed face x = 0, variable in time, is considered. Through several transformations the problem is reduced to a free boundary problem for a diffusion equation and the integral formulation is obtained. By using fixed point theorems, the existence of at least a solution, for small time, to a system of coupled nonlinear integral equations is obtained. Highlights: We study a nonlinear free boundary problem for a diffusion–convection equation with a Dirichlet condition, variable in time, at fixed face. We reduce it to another free boundary problem for heat-diffusion equation. An integral formulation to the problem which requires to solve a system of coupled nonlinear Volterra integral equations is obtained. We use the Banach and the Schauder fixed point theorems to prove existence of at least a solution.