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Zeitschrift für Analysis und ihre Anwendungen


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Volume 32, Issue 1, 2013, pp. 37–53
DOI: 10.4171/ZAA/1473

Published online: 2013-01-27

Transport Equations with Fractal Noise - Existence, Uniqueness and Regularity of the Solution

Elena Issoglio[1]

(1) King's College London, UK

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.

Keywords: Transport equation, non-smooth coefficients, fractional Brownian noise, stochastic partial differential equation

Issoglio Elena: Transport Equations with Fractal Noise - Existence, Uniqueness and Regularity of the Solution. Z. Anal. Anwend. 32 (2013), 37-53. doi: 10.4171/ZAA/1473