STOCHASTIC POROUS MEDIA EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10190421" target="_blank" >RIV/00216208:11320/13:10190421 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1142/S021949371350010X" target="_blank" >http://dx.doi.org/10.1142/S021949371350010X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S021949371350010X" target="_blank" >10.1142/S021949371350010X</a>

Result language
angličtina
Original language name
STOCHASTIC POROUS MEDIA EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION
Original language description
The present work deals with stochastic porous media equation with multiplicative noise, driven by fractional Brownian motion B-(H) with Hurst index H > 1/2. The stochastic integral with integrator B-(H) is defined pathwise following the theory developedby Zahle [24], based on the so-called fractional derivatives. It is shown that there is a one-to-one correspondence between solutions to the stochastic equation and solutions to its deterministic counterpart. By means of this correspondence and exploiting properties of the deterministic porous media equation, the existence, uniqueness, regularity and long-time properties of the solution is established. We also prove that the solution forms a random dynamical system in an appropriate function space.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F10%2F0752" target="_blank" >GAP201/10/0752: Stochastic Space-Time Systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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