36. chen.foondun.ea:23:global#
Global solution for superlinear stochastic heat equation on \(\mathbb{R}^d\) under Osgood-type conditions
Le Chen, Mohammud Foondun, Jingyu Huang, and Michael Salins
To appear in Nonlinearity
Abstract: We study the stochastic heat equation (SHE) on \(\mathbb{R}^d\) subject to a centered Gaussian noise that is white in time and colored in space.The drift term is assumed to satisfy an Osgood-type condition and the diffusion coefficient may have certain related growth. We show that there exists a random field solution that does not explode in finite time. This complements and improves upon recent results on blow-up of solutions to stochastic partial differential equations.
Keywords. Global solution; stochastic heat equation; reaction-diffusion; Dalang’s condition; superlinear growth; Osgood-type conditions.
[CFHS23] Le Chen, Mohammud Foondun, Jingyu Huang & Michael Salins (2023) ‘Global solution for superlinear stochastic heat equation on \(\mathbb{R}^d\) under Osgood-type conditions’, preprint arXiv:2310.02153
@article{chen.foondun.ea:23:global,
title = {Global solution for superlinear stochastic heat equation on $\mathbb{R}^d$ under Osgood-type conditions},
author = {Le Chen and Mohammud Foondun and Jingyu Huang and Michael Salins},
year = {2023},
month = {October},
journal = {preprint arXiv:2310.02153},
url = {http://arXiv.org/abs/2310.02153}
}
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