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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F13%3A10190421%21RIV14-GA0-11320___
rdf:type
n15:Vysledek skos:Concept
rdfs:seeAlso
http://dx.doi.org/10.1142/S021949371350010X
dcterms: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 developed by 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. 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 developed by 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.
dcterms:title
STOCHASTIC POROUS MEDIA EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION STOCHASTIC POROUS MEDIA EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION
skos:prefLabel
STOCHASTIC POROUS MEDIA EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION STOCHASTIC POROUS MEDIA EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION
skos:notation
RIV/00216208:11320/13:10190421!RIV14-GA0-11320___
n15:predkladatel
n16:orjk%3A11320
n4:aktivita
n18:P
n4:aktivity
P(GAP201/10/0752)
n4:cisloPeriodika
4
n4:dodaniDat
n10:2014
n4:domaciTvurceVysledku
n9:3512800 n9:5709296
n4:druhVysledku
n19:J
n4:duvernostUdaju
n13:S
n4:entitaPredkladatele
n11:predkladatel
n4:idSjednocenehoVysledku
108033
n4:idVysledku
RIV/00216208:11320/13:10190421
n4:jazykVysledku
n5:eng
n4:klicovaSlova
random dynamical system; stochastic porous media equation; Fractional Brownian motion
n4:klicoveSlovo
n7:stochastic%20porous%20media%20equation n7:random%20dynamical%20system n7:Fractional%20Brownian%20motion
n4:kodStatuVydavatele
SG - Singapurská republika
n4:kontrolniKodProRIV
[2094CBA91B28]
n4:nazevZdroje
Stochastics and Dynamics
n4:obor
n17:BA
n4:pocetDomacichTvurcuVysledku
2
n4:pocetTvurcuVysledku
3
n4:projekt
n21:GAP201%2F10%2F0752
n4:rokUplatneniVysledku
n10:2013
n4:svazekPeriodika
13
n4:tvurceVysledku
Bártek, Jan Maslowski, Bohdan Garrido-Atienza, Maria J.
n4:wos
000325407900007
s:issn
0219-4937
s:numberOfPages
33
n14:doi
10.1142/S021949371350010X
n12:organizacniJednotka
11320