On inverse problems for strongly degenerate parabolic equations under the integral observation condition

Existence and uniqueness theorems for inverse problems of determining the right-hand side and lowest coefficient in a degenerate parabolic equation with two independent variables are proved. It is assumed that the leading coefficient of the equation degenerates at the side boundary of the domain and the order of degeneracy with respect to the variable $x$ is not lower than $2$. Thus, the Black–Scholes equation, well-known in financial mathematics, is admitted. These results are based on the study of the unique solvability of the corresponding direct problem, which is also of independent interest.