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Nonlocal Kolmogorov–Petrovskii–Piskunov and Fisher equation on a closed manifold and its solutionsстатья
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 28 мая 2025 г.
- Авторы: Davydov Alexey, Platov Anton, Tunitsky Dmitry
- Журнал: Central European Journal of Operations Research
- Том: 33
- Номер: 2
- Год издания: 2025
- Издательство: Physica-Verlag Gmbh und Co.
- Местоположение издательства: Germany
- Первая страница: 537
- Последняя страница: 548
- DOI: 10.1007/s10100-025-00975-y
- Аннотация: We study the dynamics of a resource distributed on a closed smooth manifold, forexample, on a two-dimensional sphere—the Earth’s surface. It is assumed that thisdynamics is described by the nonlocal Kolmogorov–Petrovskii–Piskunov and Fisherequation, the nonlocality of which is expressed by the dependence of the reactionterm of the equation on the integral of the product of the sought solution with someintegral kernel over the manifold. For example, if this kernel is equal to one, weobtain the dependence of the reaction term on the total volume of the resource onthe manifold. Under natural restrictions on the parameters of the equation, a uniqueness theorem for the Caushy problem is proved f on assumption that initial data is bounded and nonnegative, and the solution has a continuous L2-norm for nonegative t and is bounded.
- Добавил в систему: Давыдов Алексей Александрович