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

Dai Noboriguchi

doi:10.1090/tpms/1212

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

Dai Noboriguchi^*

^*Corresponding author for this work

Waseda University Senior High School

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we are interested in the initial Dirichlet boundary value problem for a transport equation driven by weak geometric Hölder 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.

Original language	English
Pages (from-to)	167-183
Number of pages	17
Journal	Theory of Probability and Mathematical Statistics
Volume	110
DOIs	https://doi.org/10.1090/tpms/1212
Publication status	Published - 2024

Keywords

Initial-boundary value problem
rough paths
transport equation

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1090/tpms/1212

Cite this

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abstract = "In this paper, we are interested in the initial Dirichlet boundary value problem for a transport equation driven by weak geometric H{\"o}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.",

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

Abstract

Keywords

ASJC Scopus subject areas

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