2021/11/21 by Gregorio Díaz, Gregorio Díaz Díaz, Jesús Ildefonso Díaz +4 · 1 citation
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #35R60 #60H15 #60H30 #86A08 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.AP #math.PR #msc:35R60 #msc:60H15 #msc:60H30 #msc:86A08
paper · pdf · doi:10.48550/arxiv.2111.10801
33 pages and one figure
openalex publication_date 2021/11/21 · arxiv created 2021/12/22 · arxiv updated 2021/12/23 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We consider a class of one-dimensional nonlinear stochastic parabolic problems associated with 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.