{'fraction_non_alphanumeric': 0.015789473684210527, 'fraction_numerical': 0.0, 'mean_word_length': 5.274725274725275, '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}}
Evolution equations with monotone operator and functional non-linearity at the time derivative

Conditions for the solubility of the so-called doubly non-linear equations are investigated. Here is a monotone operator induced by a differential expression containing higher-order partial derivatives and is an operator induced by a monotone function. A theorem on the existence of a solution is proved. The method of monotone operators is used in combination with the method of compact operators. Examples of applications to parabolic differential equations are presented.