Inverse problems of determining coefficients of time type in a degenerate parabolic equation

Abstract

The paper is devoted to the study of the solvability of inverse coefficient problems for degenerate parabolic equations of the second order. We study both linear inverse problems - the problems of determining an unknown right-hand side (external influence), and nonlinear problems of determining an unknown coefficient of the equation itself. The peculiarity of the studied work is that its unknown coefficients are functions of a time variable only. The work aims to prove the existence and uniqueness of regular solutions to the studied problems (having all the generalized in the sense of S.L. Sobolev derivatives entering the equation).

Keywords

• degenerate parabolic equations
• linear inverse problems
• non-linear inverse problems
• regular solutions
• existence