Issoglio, E (2013) Transport equations with fractal noise – existence, uniqueness and regularity of the solution. Zeitschrift für Analysis und ihre Anwendungen, 32 (1). pp. 37-53. ISSN 0232-2064
Abstract
The main result of the present paper is a statement on existence, uniqueness and regularity for mild solutions to a parabolic transport diffusion type equation that involves a non-smooth coefficient. We investigate related Cauchy problems on bounded smooth domains with Dirichlet boundary conditions by means of semigroup theory and xed point arguments. Main ingredients are the de nition of a product of a function and a (not too irregular) distribution as well as a corresponding norm estimate. As an application, transport stochastic partial differential equations driven by fractional Brownian noises are considered in the pathwise sense.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, EMS Publishing House. This is an author produced version of a paper published in Zeitschrift für Analysis und ihre Anwendungen. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Transport equation; non-smooth coefficients; fractional Brownian noise; stochastic partial differential equation |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Aug 2016 15:10 |
Last Modified: | 17 Jan 2018 21:08 |
Published Version: | http://dx.doi.org/10.4171/ZAA/1473 |
Status: | Published |
Publisher: | European Mathematical Society |
Identification Number: | 10.4171/ZAA/1473 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:98921 |