{'fraction_non_alphanumeric': 0.015063731170336037, 'fraction_numerical': 0.0, 'mean_word_length': 5.171428571428572, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
ON CERTAIN INVERSE PROBLEMS FOR PARABOLIC EQUATIONS WITH FINAL AND INTEGRAL OBSERVATION

The inverse problems of finding the free term and the coefficient of u(x,t) in a parabolic equation is considered. The Fredholm property of the linear inverse problem of finding the right-hand side of a special form is proved, along with global existence, uniqueness, and stability theorems for its solutions. A uniqueness theorem is established for the nonlinear inverse problem of determining the coefficient under restrictions in the form of inequalities containing no smallness conditions. The proof is carried out by a method of a priori estimates, with the use of the maximum principle for parabolic and elliptic equations. A connection between the uniqueness of the solution of the inverse problem and the completeness of a certain system of functions is established.