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We study existence and uniqueness of distributional solutions to the stochastic partial differential equation $dX - ( u Delta X + Delta psi (X) ) dt = sum_{i=1}^N langle b_i, abla X rangle circ dbeta_i$ in $]0,T[ times mathcal{O}$, with $X(0) = x(xi)$ in $mathcal{O}$ and $X = 0$ on $]0,T[ times partial mathcal{O}$. Moreover, we prove extinction in finite time of the solutions in the special case of fast diffusion model and of self-organized criticality model.
We establish finite time extinction with probability one for weak solutions of the Cauchy-Dirichlet problem for the 1D stochastic porous medium equation with Stratonovich transport noise and compactly supported smooth initial datum. Heuristically, th
The purpose of this paper is extend recent results of Bonder-Groisman and Foondun-Nualart to the stochastic wave equation. In particular, a suitable integrability condition for non-existence of global solutions is derived.
In this paper we investigate existence of solutions for the system: begin{equation*} left{ begin{array}{l} D^{alpha}_tu=textrm{div}(u abla p), D^{alpha}_tp=-(-Delta)^{s}p+u^{2}, end{array} right. end{equation*} in $mathbb{T}^3$ for $0< s leq 1$, and
We delve deeper into the study of semimartingale attractors that we recently introduced in Allouba and Langa cite{AL0}. In this article we focus on second order SPDEs of the Allen-Cahn type. After proving existence, uniqueness, and detailed regularit
In order to analyze numerically inverse problems several techniques based on linear and nonlinear stability analysis are presented. These techniques are illustrated on the problem of estimating mobilities and capillary pressure in one-dimensional two