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0516U000120,
д.ф.-м.н.
16-02-2016
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The Cauchy and nonlocal problems for parabolic pseudodifferential equations with nonsmooth symbols
Drin Yaroslav Mykhailovych,
popup.head Gorodetskyi Vasyl Vasylovych
popup.opponent Горбачук Мирослав Львович
popup.opponent Іванчов Микола Іванович
popup.opponent Слюсарчук Василь Юхимович
Побудовано теорію коректної розв'язності нелокальної багатоточкової за часом задачі для еволюційних псевдодиференціальних рівнянь скінченного та нескінченного порядків з ПДО, визначеними у різних просторах гладких функцій. Розвинено методику дослідження ФРБЗ, встановлено їх структуру та властивості, знайдено умови коректної визначеності оператора , де - ціла функція від ПДО A. Доведено теореми про коректну роз'язність нелокальної багатоточкової за часом задачі для еволюційних ПДО з точково-негладкими однорідними символами та гладкими символами у випадку, коли гранична функція належить до певного класу узагальнених функцій типу розподілів. Побудовано розв'язок задачі Коші для квазілінійних B-параболічних диференціальних рівнянь з відхиленням аргументу, а також розв'язок задачі Коші і нелокальних задач для псевдодиференціальних квазілінійних рівнянь з відхиленням аргументу, які розв'язуються методом кроків. Досліджено пряму й обернену задачі для одного класу еволюційних ПДР методом неповного відокремлення змінних та із застосуванням гібридних інтегральних перетворень Фур'є класичного за просторовими змінними та узагальненого за півпросторовою змінною.
2016-02-16
2020-04-03
Updated: 2025-12-09
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