Free Boundary Problem for a Nonlinear Diffusion Equation
DOI:
https://doi.org/10.56143/ujmcs.v1i2.10Keywords:
квазилинейное параболическое уравнение; свободная граница; априорные оценки; теорема существования и единственности.Abstract
In this paper, a Stefan-type problem with two free boundaries for a nonlinear heat equation in the one-dimensional case is considered. The study of nonlinear problems with free boundaries is carried out using a method based on constructing a priori estimates. In this regard, some initial a priori estimates are first established for solving the problem under consideration. Then, the problem is reduced to a problem with a fixed boundary through a change of variables. The resulting problem has time- and position-dependent coefficients with nonlinear terms. Next, a priori estimates of the Schauder type are constructed for solving the equation with nonlinear terms and a fixed boundary. Based on the estimates obtained, the solvability of the original problem is established.
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