Effects of Additive and Multiplicative Noise on the Dynamics of a Parabolic Equation

Authors

Tom?s Caraballo, Dpto. Ecuaciones Diferenciales y An´alisis Num´erico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, SpainFollow
Renato Colucci, Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, 111 Ren’ai Road, Suzhou, , 215123, P. R. ChinaFollow

Author Country (or Countries)

P. R. China

Abstract

We consider the effects of additive and multiplicative noise on the asymptotic behavior of a fourth order parabolic equation arising in the study of phase transitions. On account that the deterministic model presents three different time scales, in this paper we have established some conditions under which the third time scale, which encounter finite dimensional behavior of the system, is preserved under both additive and multiplicative linear noise. In particular we have proved the existence of a random attractor in both cases, and observed that the order of magnitude of the third time scale is also preserved.

Recommended Citation

Caraballo, Tom?s and Colucci, Renato (2023) "Effects of Additive and Multiplicative Noise on the Dynamics of a Parabolic Equation," Applied Mathematics & Information Sciences: Vol. 09: Iss. 5, Article 8.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/8