Pathwise Blowup of space-time fractional SPDEs

TL;DR

This paper investigates the conditions under which certain space-time fractional stochastic partial differential equations experience finite-time blowup, extending previous results to broader noise types and spatial domains.

Contribution

It provides new necessary and sufficient conditions for blowup in bounded domains and sufficient conditions for blowup in unbounded domains for space-time fractional SPDEs.

Findings

Blowup occurs under specific Osgood conditions in bounded domains.

Sufficient conditions for blowup are established for the whole space case.

Results extend previous work by Foondun and Nualart (2021).

Abstract

The finite time blowup in the almost sure sense of a class of space-time fractional stochastic partial differential equations is discussed. Both the cases of white noise and colored noise are considered. The sufficient and necessary condition between the blowup and Osgood condition is obtained when the spatial domain is bounded. And the sufficient condition for the blowup is obtained when the spatial domain is the whole space. The results in this paper could be regarded as extensions to some results in Foondun and Nualart, 2021.