# Global solutions to the stochastic heat equation with superlinear accretive reaction term and superlinear multiplicative noise term on a bounded spatial domain

@inproceedings{Salins2021GlobalST, title={Global solutions to the stochastic heat equation with superlinear accretive reaction term and superlinear multiplicative noise term on a bounded spatial domain}, author={Michael Salins}, year={2021} }

We describe sufficient conditions on the reaction terms and multiplicative noise terms of a stochastic reaction-diffusion equation that guarantee that the solutions never explode. Both the reaction term and multiplicative noise terms are allowed to grow superlinearly.

## References

SHOWING 1-10 OF 27 REFERENCES

Long time existence for the heat equation with a noise term

- Mathematics
- 1991

SummaryWe consider the equationut=uxx+uγ W forx on a finite interval, with Dirichlet boundary conditions. W is spacetime white noise. The initial condition is continuous and nonnegative. We show…

On quasi-linear stochastic partial differential equations

- Mathematics
- 1993

SummaryWe prove existence and uniqueness of the solution of a parabolic SPDE in one space dimension driven by space-time white noise, in the case of a measurable drift and a constant diffusion…

On uniqueness of mild solutions for dissipative stochastic evolution equations

- Mathematics
- 2010

In the semigroup approach to stochastic evolution equations, the fundamental issue of uniqueness of mild solutions is often "reduced" to the much easier problem of proving uniqueness for strong…

Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term

- Mathematics
- 2003

Abstract We study existence and uniqueness of a mild solution in the space of continuous functions and existence of an invariant measure for a class of reaction-diffusion systems on bounded domains…

Long time existence for the wave equation with a noise term

- Mathematics
- 1997

We consider the equationut=uxx+uγ W forx on a finite interval, with Dirichlet boundary conditions. W is spacetime white noise. The initial condition is continuous and nonnegative. We show existence…

Global Solutions to Stochastic Wave Equations with Superlinear Coefficients

- Mathematics
- 2019

We prove existence and uniqueness of a random field solution $(u(t,x); (t,x)\in [0,T]\times \mathbb{R}^d)$ to a stochastic wave equation in dimensions $d=1,2,3$ with diffusion and drift coefficients…

Global solutions to stochastic reaction–diffusion equations with super-linear drift and multiplicative noise

- MathematicsThe Annals of Probability
- 2019

Let ξ(t , x) denote space-time white noise and consider a reaction-diffusion equation of the form u̇(t , x) = 12u ′′(t , x) + b(u(t , x)) + σ(u(t , x))ξ(t , x), on R+ × [0 , 1], with homogeneous…

Non-existence for stochastic wave equations in one dimension

- Mathematics
- 2020

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-existence of…

The critical parameter for the heat equation with a noise term to blow up in finite time

- Mathematics
- 1999

Consider the stochastic partial differential equation u t = u xx + u γ W, where x E I ≡ [0, J], W = W(t, x) is 2-parameter white noise, and we assume that the initial function u(0, x) is nonnegative…