parabolic equation, inverse problem, initial-boundary value problem, existence, uniqueness
Abstract
In the article we examine the question of regular solvability in Sobolev spaces of parabolic inverse coefficient problems. A solution is sought in the class of regular solutions that has all derivatives occurring in the equation summable to some power. The overdetermination conditions are the values of a solution at some collection of points lying inside the domain. The proof is based on a priori estimates and the fixed point theorem.
Author Biographies
Sergey Grigorievich Pyatkov, Yugra State University, Khanty-Mansiysk
Dr. Sc. (Physics and Mathematics), Professor, School of Digital Engineering
Oleg Al’bertovich Soldatov, Yugra State University, Khanty-Mansiysk
