Multipoint Initial-Final Problem for One Class of Sobolev Type Models of Higher Order with Additive "White Noise"
DOI:
https://doi.org/10.14529/mmp180308Ключевые слова:
уравнение соболевского типа, пропагатор, "белый шум".Аннотация
Теория уравнений Соболева была предметом интереса многих исследователей последние годы, при этом много внимания уделялось детерминированным уравнениям и системам. Тем не менее, существуют также математические модели, содержащие случайные возмущения, такие как белый шум. Новая концепция "белого шума", первоначально построенная для конечномерных пространств, в данной работе распространяется на случай бесконечномерных пространств. Основная цель заключается в разработке стохастической теории уравнений cоболевского типа высокого порядка и предоставлении некоторых практических приложений. Основная идея состоит в том, чтобы построить пространства 'шумов', используя производную Нельсона - Гликлиха. Абстрактные результаты, касающиеся начально-конечных задач для уравнений cоболевского типа высокого порядка, применяются к математической модели Буссинеска - Лява с аддитивным 'белым шумом'. Использован такой известный метод теории уравнений cоболевского типа, как метод фазового пространства, заключающийся в редукции сингулярного уравнения к регулярному, определенному на некотором подпространстве исходного пространства, понимаемом как фазовое пространство.Библиографические ссылки
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