Local Existence of a Solution to a One-Phase Stefan Problem with Advection and a Boundary Heat Flux
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We study the Stefan problem with advection for a non-classical heat equation that includes a heat flux at the boundary. The objective is to determine the temperature distribution and the location of the moving phase boundary under given initial and boundary conditions. The existence and uniqueness of solutions are analyzed using the unified transform method, referred to as the Fokas method, and the Friedman-Rubinstein approach, which establishes local existence and uniqueness in an appropriate Banach space. The results offer valuable insights into the mathematical structure of Stefan problems involving both advection and boundary heat flux.
Abstract
We study the Stefan problem with advection for a non-classical heat equation that includes a heat flux at the boundary. The objective is to determine the temperature distribution and the location of the moving phase boundary under given initial and boundary conditions. The existence and uniqueness of solutions are analyzed using the unified transform method, referred to as the Fokas method, and the Friedman-Rubinstein approach, which establishes local existence and uniqueness in an appropriate Banach space. The results offer valuable insights into the mathematical structure of Stefan problems involving both advection and boundary heat flux.