Keywords: Climate Nonlinear diffusive energy balance model Non-degenerate solution Finite elements 2-sphere a b s t r a c t The purpose of this paper is to carry out the mathematical and numerical… (More)

In this paper we prove an approximate controllability result for an abstract semilinear evolution equation in a Hilbert space and we obtain as consequences the approximate controllability for some… (More)

Energy balance climate models of Budyko type lead to reaction–diffusion equations with slow diffusion and memory on the 2-sphere. The reaction part exhibits a jump discontinuity (at the snow line).… (More)

We study the differentiability of very weak solutions v ∈ L1(Ω) of (v,L φ)0 = (f,φ)0 for all φ ∈ C2(Ω) vanishing at the boundary whenever f is in L1(Ω, δ), with δ = dist(x, ∂Ω), and L∗ is a linear… (More)

We study the existence and multiplicity of solutions, strictly positive or nonnegative having a free boundary (the boundary of the set where the solution vanishes) of some one-dimensional quasilinear… (More)

We propose a modi cation of the classical Navier-Stokes-Boussinesq system of equations, which governs buoyancy-driven ows of viscous, incompressible uids. This modi cation is motivated by… (More)

We get some necessary and sufficient conditions for the very weak solvability of the beam equation stated in terms of powers of the distance to the boundary, accordingly to the boundary condition… (More)

This paper is concerned with the elliptic system ∆v = φ, ∆φ = |∇v|2, (0.1) posed in a bounded domain Ω ⊂ RN , N ∈ N . Specifically, we are interested in the existence and uniqueness or multiplicity… (More)