粗糙路径驱动的传输方程的初始边界值问题

Pub Date : 2024-05-10 DOI:10.1090/tpms/1212

Dai Noboriguchi

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引用次数: 0

摘要

在本文中，我们关注的是由弱几何荷尔德 p p - 通过路径驱动的传输方程的初始 Dirichlet 边界值问题。我们引入了带边界条件的粗糙偏微分方程解的概念。因此，我们将在下文所述的一些假设条件下建立这样一个解的好求解性。此外，我们还将明确给出解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Initial-boundary value problem for transport equations driven by rough paths

In this paper, we are interested in the initial Dirichlet boundary value problem for a transport equation driven by weak geometric Hölder p p -rough paths. We introduce a notion of solutions to rough partial differential equations with boundary conditions. Consequently, we will establish a well-posedness for such a solution under some assumptions stated below. Moreover, the solution is given explicitly.

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