Show simple item record

dc.contributor.advisorNane, Erkan
dc.contributor.authorGuerngar, Ngartelbaye
dc.date.accessioned2019-07-18T20:01:59Z
dc.date.available2019-07-18T20:01:59Z
dc.date.issued2019-07-18
dc.identifier.urihttp://hdl.handle.net/10415/6842
dc.description.abstractIn this dissertation, we study several stochastic partial differential equations (SPDEs) in the open and bounded domain $D$, subset of $\mathbb{R}^d$ for $d\geq 1$, driven by a multiplicative noise. We are interested in bounds and asymptotic properties of the random field solution. We study the nonlinear stochastic fractional heat equation driven by three types of noise. Existence and uniqueness of the solution is proved using a Picard iteration scheme. Upper and lower bounds on all $p^{\text{th}}$ moments, for $p\geq 2$, of the solution are obtained when the noise is spatially homogeneous (or spatially colored) with the space correlation function given by the Riesz kernel and when the noise is space-time homogeneous, with the time correlation function given by the fractional Brownian motion (fBm) while the space correlation function is given by the Riesz kernel in space. We also show that under exterior boundary conditions, in the long run, the $p^{\text{th}}$-moment of the solution grows exponentially fast for large values of the noise level. However, for small values of the noise level, we observe eventually an exponential decay of the $p^{\text{th}}$-moment of this solution.en_US
dc.subjectMathematics and Statisticsen_US
dc.titlePhase transition for fractional stochastic partial differential equations in a bounded domainen_US
dc.typePhD Dissertationen_US
dc.embargo.lengthen_US
dc.embargo.statusNOT_EMBARGOEDen_US


Files in this item

Show simple item record