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Stochastic energy balance climate models with Legendre weighted diffusion and an additive cylindrical Wiener process forcing

  • *Corresponding author: Jesús Ildefonso Díaz

    *Corresponding author: Jesús Ildefonso Díaz

Dedicated to Georg Hetzer on occasion of his 75th birthday

Partially supported the UCM Research Group MOMAT (ref. 910480) and the projects MTM2017-85449-P and PID2020-112517GB-I00 of the DGISPI, Spain

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  • 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.

    Mathematics Subject Classification: 60H15, 60H30, 35R60, 86A08.


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  • Figure 1.  Values of the parameter $ {{\rm{Q}}} $ with different multiplicity

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