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

Noboriguchi, Dai

doi:10.1090/tpms/1212

Author: Dai Noboriguchi
Journal: Theor. Probability and Math. Statist. 110 (2024), 167-183
MSC (2020): Primary 35L04, 60H15
DOI: https://doi.org/10.1090/tpms/1212
Published electronically: May 10, 2024
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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 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.

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