INITIAL-BOUNDARY VALUE PROBLEM FOR TRANSPORT EQUATIONS DRIVEN BY ROUGH PATHS

被引：0

作者：

Noboriguchi, Dai ^{[1
]}

机构：

[1] Waseda Univ, Sr High Sch, 3-31-1 Kamishakujii,Nerima Ku, Tokyo 1770044, Japan

来源：

THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS | 2024年 / 110卷

关键词：

Initial-boundary value problem; transport equation; rough paths; SCALAR CONSERVATION-LAWS; DIFFERENTIAL-EQUATIONS;

D O I：

10.1090/tpms/1212

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we are interested in the initial Dirichlet boundary value problem for a transport equation driven by weak geometric Ho<spacing diaeresis>lder 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.

引用

页码：167 / 183

页数：17

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