21 citations · 67 across the 32 of their papers we have counts for
32 papers · 1 filter
On the local well-posedness of randomly forced reaction-diffusion equations with initial data and a superlinear reaction term
Mohammud Foondun, Davar Khoshnevisan, Eulalia Nualart
We consider a parabolic stochastic partial differential equation (SPDE) on that is forced with multiplicative space-time white noise with a bounded and Lipschitz diffusio…
On the well-posedness of SPDEs with locally Lipschitz coefficients
Mohammud Foondun, Davar Khoshnevisan, Eulalia Nualart
We consider the stochastic partial differential equation, where is defined for $(t\,,x)\in(0\,,\infty)\…
Global solution for superlinear stochastic heat equation on under Osgood-type conditions
Le Chen, Mohammud Foondun, Jingyu Huang +1
We study the \textit{stochastic heat equation} (SHE) on subject to a centered Gaussian noise that is white in time and colored in space.The drift term is assumed to satisfy…
Instantaneous everywhere-blowup of parabolic SPDEs
Mohammud Foondun, Davar Khoshnevisan, Eulalia Nualart
We consider the following stochastic heat equation \begin{equation*} \partial_t u(t\,,x) = \tfrac12 \partial^2_x u(t\,,x) + b(u(t\,,x)) + σ(u(t\,,x)) \dot{W}(t\,,x), \end{equation*…
Small ball probability estimates for the Hölder semi-norm of the stochastic heat equation
Mohammud Foondun, Mathew Joseph, Kunwoo Kim
We consider the stochastic heat equation on with periodic boundary conditions and driven by space-time white noise. Under various natural conditions, we study small ball…
Non-existence results for stochastic wave equations in one dimension
Mohammud Foondun, Eulalia Nualart
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…
The Osgood condition for stochastic partial differential equations
Mohammud Foondun, Eulalia Nualart
We study the following equation \begin{equation*} \frac{\partial u(t,\,x)}{\partial t}= Δu(t,\,x)+b(u(t,\,x))+σ\dot{W}(t,\,x),\quad t>0, \end{equation*} where is a positive con…
Remarks on a fractional-time stochastic equation
Mohammud Foondun
We consider a class of fractional time stochastic equation defined on a bounded domain and show that the presence of the time derivative induces a significant change in the qualita…
Spatial asymptotics and strong comparison principle for some fractional stochastic heat equations
Mohammud Foondun, Eulalia Nualart
Consider the following stochastic heat equation, \begin{align*} \frac{\partial u_t(x)}{\partial t}=-ν(-Δ)^{α/2} u_t(x)+σ(u_t(x))\dot{F}(t,\,x), \quad t>0, \; x \in R^d. \end{align*…
Large Deviations for a Class of Parabolic Semilinear Stochastic Partial Differential Equations in Any Space Dimension
Leila Setayeshgar
We prove the large deviation principle for the law of the solutions to a class of parabolic semilinear stochastic partial differential equations driven by multiplicative noise, in…
Some non-existence results for a class of stochastic partial differential equations
Mohammud Foondun, Wei Liu, Erkan Nane
Consider the following stochastic partial differential equation, \begin{equation*} \partial_t u_t(x)= \mathcal{L}u_t(x)+ σ(u_t(x))\dot F(t,x)\quad{t>0}\quad\text{and}\quad x\in R^d…
An approximation result for a class of stochastic heat equations with colored noise
Mohammud Foondun, Shiu-Tang Li, Mathew Joseph
We show that a large class of stochastic heat equations can be approximated by systems of interacting stochastic differential equations. As a consequence, we prove various comparis…
Large Deviations for a Class of Semilinear Stochastic Partial Differential Equations
Mohammud Foondun, Leila Setayeshgar
We prove the large deviations principle (LDP) for the law of the solutions to a class of semilinear stochastic partial differential equations driven by multiplicative noise. Our pr…
Some properties of non-linear fractional stochastic heat equations on bounded domains
Mohammud Foondun, Ngartelbaye Guerngar, Erkan Nane
Consider the following stochastic partial differential equation, \begin{equation*} \partial_t u_t(x)= \mathcal{L}u_t(x)+ ξσ(u_t(x)) \dot F(t,x), \end{equation*} where is a posi…
Non-linear noise excitation for some space-time fractional stochastic equations in bounded domains
Mohammud Foondun, Jebessa Mijena, Erkan Nane
In this paper we study non-linear noise excitation for the following class of space-time fractional stochastic equations in bounded domains: $$\partial^β_tu_t(x)=-ν(-Δ)^{α/2} u_t(x…
Asymptotic properties of some space-time fractional stochastic equations
Mohammud Foondun, Erkan Nane
Consider non-linear time-fractional stochastic heat type equations of the following type, in $(d…
On the behaviour of stochastic heat equations on bounded domains
Mohammud Foondun, Eulalia Nualart
Consider the following equation on an interval. Under Dirichlet boundary condition, we show that in t…
Moment bounds for a class of fractional stochastic heat equations
Mohammud Foondun, Wei Liu, McSylvester Omaba
We consider fractional stochastic heat equations of the form . Here denotes the noise te…
Analysis of the gradient of the solution to a stochastic heat equation via fractional Brownian motion
Mohammud Foondun, Davar Khoshnevisan, Pejman Mahboubi
Consider the stochastic partial differential equation , where denotes space-time white noise and denotes the fractional Laplace operat…
On some properties of a class of fractional stochastic heat equations
Mohammud Foondun, Wei Liu, Kuanhou Tian
We consider nonlinear parabolic stochastic equations of the form $\partial_t u=\sL u + λσ(u)\dot ξ$ on the ball , where denotes some Gaussian noise and is Li…
Mean Square Polynomial Stability of Numerical Solutions to a Class of Stochastic Differential Equations
Mohammud Foondun, Wei Liu, Xuerong Mao
The exponential stability of numerical methods to stochastic differential equations (SDEs) has been widely studied. In contrast, there are relatively few works on polynomial stabil…
Remarks on non-linear noise excitability of some stochastic heat equations
Mohammud Foondun, Mathew Joseph
We consider nonlinear parabolic SPDEs of the form on the interval , where denotes space-time white noise, is Lipschitz continuo…
On non-existence of global solutions to a class of stochastic heat equations
Mohammud Foondun, Rana Parshad
We consider nonlinear parabolic SPDEs of the form , where denotes space-time white noise. The functions and are both…
On the Stochastic Heat Equation with Spatially-Colored Random forcing
Mohammud Foondun, Davar Khoshnevisan
We consider the stochastic heat equation of the following form \frac{\partial}{\partial t}u_t(x) = (\sL u_t)(x) +b(u_t(x)) + σ(u_t(x))\dot{F}_t(x)\quad \text{for}t>0, x\in \R^d, wh…