Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity

被引：5

作者：

Salins, Michael ^{[1
]}

机构：

[1] Boston Univ, Boston, MA 02215 USA

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2022年 / 27卷

关键词：

reaction-diffusion; dissipativity; global solution; explosion; LONG-TIME EXISTENCE; HEAT-EQUATION; AVERAGING PRINCIPLE; BLOW-UP; UNIQUENESS; SYSTEMS;

D O I：

10.1214/22-EJP740

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

A condition is identified that implies that solutions to the stochastic reaction-diffusion equation aut = Au + f (u) + sigma(u)W on a bounded spatial domain never explode. We consider the case where sigma grows polynomially and f is polynomially dissipative, meaning that f strongly forces solutions toward finite values. This result demonstrates the role that the deterministic forcing term f plays in preventing explosion.

引用

页数：18

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