Inverse free boundary problem for degenerate parabolic equation

N.M. Huzyk; O.Ya. Brodyak; P.Ya. Pukach; M.I. Vovk

doi:10.15330/cmp.16.1.230-245

Authors

N.M. Huzyk Hetman Petro Sahaidachnyi National Army Academy, 32 Heroes of Maidan str., Lviv, Ukraine, 79026 https://orcid.org/0000-0002-5609-4830
O.Ya. Brodyak Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine https://orcid.org/0000-0002-9886-3589
P.Ya. Pukach Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine https://orcid.org/0000-0002-0359-5025
M.I. Vovk Lviv Polytechnic National University, 12 Bandera str., 79013, Lviv, Ukraine https://orcid.org/0000-0002-7818-7755

https://doi.org/10.15330/cmp.16.1.230-245

Keywords:

coefficient inverse problem, free boundary problem, weak power degeneration, parabolic equation, minor coefficient

Published online: 2024-06-29

Abstract

The coefficient inverse problem for a degenerate parabolic equation is studied in a free boundary domain. The degeneration of the equation is caused by time dependent function at the higher order derivative of unknown function. It is assumed that the coefficient at the minor derivative of the equation is a polynomial of the first order for the space variable with two unknown time depended functions. The conditions of existence and uniqueness of the classical solution to such inverse problem are established for the weak degeneration case at the Dirichlet boundary conditions and the values of heat moments as overdetermination conditions.

Inverse free boundary problem for degenerate parabolic equation

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