Abstract
We study existence and uniqueness of the solution for the inverse problem of determination of the unknown coefficient ϱ(t) multiplying u t in a nondivergence parabolic equation. As additional information, the integral of the solution over the domain of space variables with some given weight function is specified. The coefficients of the equation depend both on time and on the space variables. For this problem, we obtain sufficient conditions for the existence of generalized solutions. We separately consider the cases of many space variables and one space variable. We prove the global uniqueness theorem for a generalized solution without any time smallness conditions.
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