INVERSE PROBLEMS FOR DEGENERATE PARABOLIC EQUATIONS WITH INTEGRAL OBSERVATION CONDITIONS

Inverse problems of recovering the right-hand side or the lowest coefficient in a multidimensional parabolic equation with weak degeneracy are considered. As an additional condition, the condition of integral observation is assumed. If this is a condition on the variables x, then functions that depend on the variable t are sought. Unknown functions are searched for in various classes (L_2, L_\infty, L_2^+, L_\infty^+). Sufficient conditions are established under which solutions exist and are unique. Estimates are given for solutions with constants explicitly written through the input data of the problems.