Exponential Dichotomies in Barenblatt-Zheltov-Kochina Model in Spaces of Differential Forms with 'Noise'
DOI:
https://doi.org/10.14529/mmp190204Ключевые слова:
уравнения соболевского типа, дифференциальные формы, стохастические уравнения, производная Нельсона - Гликлиха.Аннотация
Исследована устойчивость решений в линейных стохастических моделях соболевского типа с относительно ограниченным оператором в пространствах гладких дифференциальных форм, определенных на гладких компактных ориентированных римановых многообразиях без края. Для этого в пространстве дифференциальных форм используем вместо обычного оператора Лапласа псевдодифференциальный оператор Лапласа - Бельтрами. В качестве начальных использованы условие Коши и условие Шоуолтера - Сидорова. В связи с недифферинцируемостью, в обычном понимании, имеющегося в модели 'белого шума' используем производную стохастического процесса в смысле Нельсона - Гликлиха. Для исследования устойчивости решений устанавливаем наличие экспоненциальных дихотомий разделяющих пространство решений на устойчивое и неустойчивое инвариантные подпространства. В качестве примера используется стохастический вариант уравнения Баренблатта - Желтова - Кочиной в пространстве дифференциальных форм, определенных на гладком компактном ориентированном римановом многообразии без края.Библиографические ссылки
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