This article is cited in 1 paper

Free boundary problem for a system of parabolic equations of the reaction-diffusion type

M. S. Rasulov<sup>ab

a</sup> V.I. Romanovskiy Institute of Mathematics Uzbekistan Academy of Sciences, 9 University str., Tashkent, 100174 Republic of Uzbekistan
^b "TIIAME" National Research University, 39 Kori Niyozov str., Tashkent, 100000 Republic of Uzbekistan

Abstract: This paper considers a free boundary problem for a system of quasi-linear parabolic equations in one dimension. Nonlinear problems with a free boundary are studied using a method based on constructing a priori estimates. For the solutions of the problem, apriory estimates of Shauder type are established. On the base of apriory estimates, the existence and uniqueness theorems are proved.

Keywords: reaction-diffusion type, parabolic equation, free boundary, a priori estimate, existence and uniqueness theorem.

UDC: 517.956.4

Received: 24.01.2024
Revised: 24.01.2024
Accepted: 20.03.2024

DOI: 10.26907/0021-3446-2025-2-79-90

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2025, 69:2, 56–66