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Интеллектуальная Система Тематического Исследования НАукометрических данных |
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Nonlinear equations of mathematical physicsучебный курс
- Автор: Розанова Ольга Сергеевна
- Год создания: 2017
- Организация: МГУ имени М.В. Ломоносова
- Курс на иностранном языке
- Описание: This course is devoted to the presentation of classical and recent results of the theory of nonlinear partial differential equations. First of all, we consider first order quasi-linear equations and systems of conservation laws, in particular, the systems which are used to model many continuous media. We discuss the issues of singularity formation, the construction of shock wave solutions and their regularization, large time asymptotics. Then we consider equations of higher orders which model important processes in physics and biology. Among them are the Kolmogorov-Petrovskii-Piskunov equation, Korteweg-de Vries equation, nonlinear Schrödinger equation, and nonlinear heat conduction equations. We discuss traveling wave solutions, formation and propagation of singularities, solitons, the localization of heat fronts. The course aims to familiarize the audience with the most striking phenomena of the theory of nonlinear equations.
- Добавил в систему: Розанова Ольга Сергеевна