Contemporary Mathematics. Fundamental DirectionsContemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направления2413-36392949-0618Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)32588ArticlesСтатьиResearch ArticlePseudo-Parabolic Regularization of Forward-Backward Parabolic Equations with Bounded NonlinearitiesПсевдопараболическая регуляризация возвратно-поступательных параболических уравнений с ограниченными нелинейностямиTeseiAlbertoТесеиА.albertotesei@gmail.comIstituto per le Applicazioni del Calcolo «M. Picone» Consiglio Nazionale delle Ricerche1512201660VOL 60, NO (2016)ТОМ 60, № (2016)16418314112022Copyright ©; 2022, Contemporary Mathematics. Fundamental DirectionsCopyright ©; 2022, Современная математика. Фундаментальные направления2022Contemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направленияhttps://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/CMFD/article/view/32588We study the initial-boundary value problem, with Radon measure-valued initial data, by assuming that the regularizing term ψ is increasing and bounded (the cases of power-type or logarithmic ψ were dealt with in [2, 3] in any space dimension). The function ϕ is nonmonotone and bounded, and either (i) decreasing and vanishing at in nity, or (ii) increasing at in nity. Existence of solutions in a space of positive Radon measures is proven in both cases. Moreover, a general result proving spontaneous appearance of singularities in case (i) is given. The case of a cubic-like ϕ is also discussed, to point out the in uence of the behavior at in nity of ϕ on the regularity of solutions.Изучается начально-краевая задача с начальными данными, имеющими значениями меры Радона, при условии, что регуляризирующий член ψ возрастает и ограничен (случаи степенного и логарифмического ψ рассмотрены в [2, 3] для пространства любой размерности). Функция ϕ немонотонна и ограничена, а на бесконечности она либо убывает и обращается в нуль, либо возрастает. Для обоих случаев доказывается существование решений в пространстве положительных мер Радона. Кроме того, для первого случая устанавливается общий результат о спонтанном возникновении особенностей. Чтобы отметить влияние поведения функции ϕ на бесконечности на регулярность решений, рассматривается также и случай, когда ϕ ведет себя как кубическая функция.1.Barenblatt G. I., Bertsch M., Dal Passo R., Ughi M. 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