Полулинейные модели соболевского типа. Неединственность решения задачи Шоуолтера - Сидорова

Статья имеет обзорный характер и содержит результаты исследования морфологии фазовых пространств полулинейных моделей соболевского типа. Представлены исследования тех математических моделей, чьи фазовые пространства лежат на гладких банаховых многообразиях с особенностями в зависимости от параметров задачи, а именно модели Хоффа, модели Плотникова, модели распределенного брюсселятора и модели распространения нервного импульса. В первой части статьи приведены условия, при которых фазовые многообразия изучаемых моделей - простые гладкие банаховы многообразия, из чего вытекает единственность решения задачи Шоуолтера - Сидорова. Во второй части статьи приведены условия, при которых фазовые многообразия исследуемых моделей содержат особенности, из чего вытекает неединственность решения задачи Шоуолтера - Сидорова.

Ключевые слова

уравнения соболевского типа; фазовое пространство; морфология фазового пространства; банаховы многообразия; задача Шоуолтера - Сидорова; k-сборка Уитни.

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