논문KCI 등재
Heat equation with a geometric rough path potential in one space dimension: existence and regularity of solution
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
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.
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.
참고문헌 (8)
- P. Friz, "A Course on Rough Paths" (2014), Springer
- Martin Hairer, "A simple construction of the continuum parabolic Anderson model on R2", Electronic Communications in Probability, 20 (2015), Institute of Mathematical Statistics[DOI]
- Yaozhong Hu, "Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency", Electronic Journal of Probability, 20 (2015), Institute of Mathematical Statistics[DOI]
- H.-J. Kim, "Time-homogeneous parabolic Wick–Anderson model in one space dimension: regularity of solution", Stochastics and Partial Differential Equations: Analysis and Computations, 5(4), pp.559~591 (2017), Springer Science and Business Media LLC[DOI]
- N. V. Krylov, "Lectures on Elliptic and Parabolic Equations in Holder spaces", pp.1090~ (1996), American Mathematical Society
- O. A. Ladyzenskaja, "Translations of Mathematical Monographs, Vol. 23" (1968), American Mathematical Society
- A. M. Savchuk, "Sturm-liouville operators with singular potentials, Math. Notes 66 (1999), no. 5-6, 741-753 (2000)", Mathematical Notes, 66(6), pp.741~753 (1999), Springer Science and Business Media LLC[DOI]
- E. Wong, "On the convergence of ordinary integrals to stochastic integrals", Ann. Math. Statist, 36, pp.1560~1564 (1965)[DOI]
관련 논문AI추천
Some stability results for semilinear stochastic heat equation driven by a fractional noiseOussama El Barrimi, Youssef Ouknine대한수학회 · 대한수학회보2019 · 제56권 제3호NOTE ON ABSTRACT STOCHASTIC SEMILINEAR EVOLUTION EQUATIONSTˆon Viˆe. TA대한수학회 · 대한수학회지2017 · 제54권 제3호A random dispersion Schrodinger equation with nonlinear time-dependent loss/gainBin Liu, Hui Jian대한수학회 · 대한수학회보2017 · 제54권 제4호Stochastic differential equations driven by an additive fractional Brownian sheetOussama El Barrimi, Youssef Ouknine대한수학회 · 대한수학회보2019 · 제56권 제2호Solution formulas for some nonlocal heat equations허형진대한수학회 · 대한수학회논문집2016 · 제31권 제3호A note on the generalized heat content for L\'{e}vy processesTomasz Grzywny, Wojciech Cygan대한수학회 · 대한수학회보2018 · 제55권 제5호
이 간행물의 다른 논문 (24건)
The $U$-projective resolution of modules over path algebras of types $A_n$ and $\tilde{A}_n$Karin Baur, Intan Muchtadi-Alamsyah, Yudi Mahatmapp. 701-718On partial-Armendariz rings윤상조, Zhelin Piao, 남상복pp. 719-727On prime submodules of a finitely generated projective module over a commutative ringZahra Pourshafiey, Reza Nekooeipp. 729-741Module amenability and module Arens regularity of weighted semigroup algebrasAbasalt Bodaghi, DAVOOD EBRAHIMI BAGHA, Gholamreza Asgaripp. 743-755Generalizations of Alesandrov problem and Mazur-Ulam theorem for two-isometries and two-expansive mappingsAbdulqader Mohammadi, Hamid Khodaeipp. 771-782