Displaying similar documents to “On a stochastic parabolic PDE arising in climatology.”

A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.

J. I. Díaz, L. Tello (1999)

Collectanea Mathematica

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We present some results on the mathematical treatment of a global two-dimensional diffusive climate model. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature. The spatial domain is a compact two-dimensional Riemannian manifold without boundary simulating the Earth. We prove the existence of bounded weak solutions via a fixed point argument. Although, the uniqueness of solutions may fail, in general,...

A singular equation with positive and free boundary solutions.

Juan Dávila, Marcelo Montenegro (2003)

RACSAM

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Para 0 < β < 1 consideramos la ecuación -Δu = χ (-u + λf(x, u)) en Ω­ con condición de borde tipo Dirichlet. Esta ecuación posee una solución maximal u ≥ 0 para todo λ > 0. Si λ es menor que una cierta constante λ*, u se anula en el interior del dominio creando una frontera libre, y para λ > λ* esta solución es positiva en Ω­ y estable. Establecemos la regularidad de u incluso en presencia de una frontera libre. Para λ ≥ λ* la solución del problema parabólico...

Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions

Mireille Bossy, Mamadou Cissé, Denis Talay (2011)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper we explicit the derivative of the flows of one-dimensional reflected diffusion processes. We then get stochastic representations for derivatives of viscosity solutions of one-dimensional semilinear parabolic partial differential equations and parabolic variational inequalities with Neumann boundary conditions.