Heat equation with a geometric rough path potential in one space dimension: existence and regularity of solution
Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 757-769
Published online July 31, 2019
Hyun-Jung Kim, Sergey V. Lototsky
Illinois Institute of Technology; University of Southern California
Abstract : A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a H\"{o}lder continuous function, regularity of the resulting solution is in line with the standard parabolic theory.
Keywords : classical solution, fundamental solution, parabolic H\"{o}lder spaces, Stratonovich integral
MSC numbers : Primary 35R05; Secondary 35K20, 35D30, 60H15
Downloads: Full-text PDF   Full-text HTML


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd