The Global-in-Time Existence of a Classical Solution for Some Free Boundary Problem

Сибирский математический журнал

A. M. Meirmanov¹ 

[1] Belgorod State University

关键词: free boundary problem;    diffusion–convection equation;    fixed point method;    a priori estimate;   

DOI  :  10.1134/S0037446619020137

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We consider the problem with free (unknown) boundary for the one-dimensional diffusion–convection equation. The unknown boundary is found from the additional condition on the free boundary. A dilation of the variables reduces the problem to an initial-boundary value problem for a strictly parabolic equation with unknown coefficients in the known domain. These coefficients are found from an additional boundary condition, which makes it possible to construct a nonlinear operator whose fixed points define the solution to the initial problem.

【 授权许可】

CC BY