Open AccessStochastic energy balance climate models with Legendre weighted diffusion and an additive cylindrical Wiener process forcing
Author(s) -
Gema Alcolea-Díaz,
Jesús Ildefonso Díaz Díaz
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021165
Subject(s) - mathematics , wiener process , legendre polynomials , stochastic process , diffusion , forcing (mathematics) , stability (learning theory) , nonlinear system , energy balance , mathematical analysis , computer science , statistics , physics , thermodynamics , quantum mechanics , machine learning
We consider a class of one-dimensional nonlinear stochastic parabolic problems associated to Sellers and Budyko diffusive energy balance climate models with a Legendre weighted diffusion and an additive cylindrical Wiener processes forcing. Our results use in an important way that, under suitable assumptions on the Wiener processes, a suitable change of variables leads the problem to a pathwise random PDE, hence an essentially "deterministic" formulation depending on a random parameter. Two applications are also given: the stability of solutions when the Wiener process converges to zero and the asymptotic behaviour of solutions for large time.