21 citations · 67 across the 32 of their papers we have counts for
33 papers
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…