Erkan Nane

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math.PR2025

Space-time fractional SPDEs with locally Lipschitz coefficients: well-posedness

Ngartelbaye Guerngar, Erkan Nane

In this article, we study the space-time SPDE $\partial_{t}^{2} u = - (- I^)^{I^\pm /2} u + I_{t}^{1 - I^^{2}} [b (u) + I ¨ (u) W ˙],$ where $u = u (t, x)$ is defined for $(t,x)\in\mathbb{R}_+\times \mathbb…

math.PR2024

Propagation of high peaks for the space-time fractional stochastic partial differential equations

Ngartelbaye Guerngar, Erkan Nane

We study the space-time nonlinear fractional stochastic heat equation driven by a space-time white noise, \begin{align*} \partial_t^Î²u(t,x)=-(-Î)^{Î±/2}u(t,x)+I_t^{1-Î²}\Big[Ï(u…