Coefficient inverse problems for a degenerate differential equation with multiple characteristics

Guzel R. Ashurova

0000-0001-5053-4981

Scopus Author ID: 57428015200

1. Al-Farabi Kazakh National University, Almaty, Kazakhstan

2. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

ashurova.guzel@gmail.com

Alexander I. Kozhanov

0000-0003-4376-4003

Scopus Author ID: 55892833300

Researcher ID: 2099

1. Novosibirsk State University, Novosibirsk, Russia

2. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

kozhanov@math.nsc.ru

The paper is devoted to the investigation of solvability of new nonlinear inverse coefficient problems for third-order differential equations with multiple characteristics in anisotropic Sobolev spaces. The considered equations may degenerate at some points of the domain. Existence and uniqueness theorems for regular solutions are proved. The method is based on reduction of inverse problems to auxiliary direct problems together with regularization and a priori estimates.

УДК 517.946

Keywords: multiple characteristic differential equations, degeneration, unknown coefficient, regular solutions, existence, uniqueness.