Неклассические модели математической физики с многоточечным начально-конечным условием

Статья содержит обзор результатов авторов в области неклассических моделей математической физики, для которых рассмотрены многоточечные начально-конечные условия, обобщающие условия Коши и Шоуолтера - Сидорова. Напомним, что неклассическими называют те модели математической физики, чьи представления в виде уравнений или систем уравнений в частных производных не укладываются в рамках одного из классических типов - эллиптического, параболического или гиперболического. Абстрактные результаты проиллюстрированы конкретными многоточечными начально-конечными задачами в различных постановках для уравнений в частных производных, возникающих в последнее время в приложениях. В том числе рассмотрены неавтономная модель Чена - Гетина с комплексными коэффициентами, стохастическая эволюционная модель Девиса, макромодель транспортного потока на перекрестке, основанная на уравнениях Осколкова, рассмотренных в системе геометрических графов, учитывающих условие непрерывности, баланса потока и условие запрета на движение.

Ключевые слова

уравнения соболевского типа; разрешающие C_0-полупотоки операторов; разрешающие (полу)группы операторов; относительно спектральные проекторы; многоточечное начально-конечное условие; неавтономная модель Чена - Гетина; стохастическая модель Девиса; макромодель транспортного потока на перекрестке.

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