On domain decomposition preconditioners for finite element approximations of the Helmholtz equation using absorption.
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Abstract: We study the problem of long waves at the interface of two fluid layers of different densities and present three main results: (i) In the weak stratification (Boussinesq) case, the equations of mixed-type are well posed for times up to breaking if the initial data is in the hyperbolic region of phase space. The physical interpretation of this result is that a type of nonlinear stability holds for sufficiently large Richardson number (ii) In the general case there may be initially hyperbolic data that exit into the elliptic region (i.e. the fluid undergoes spontaneous shear...Read More
Abstract: In this talk we will consider the Landau-Lifshitz-Gilbert equation, a model describing the dynamics for the spin in ferromagnetic materials. We will discuss the Cauchy problem with initial conditions that are not in the standard Sobolev spaces, but are in the BMO (bounded mean oscillation) space. By using the stereographic projection, this problem is related to the Cauchy problem for a nonlinear Schrodinger equation with rough initial data.Read More
Abstract: (también adjunto en pdf) In this talk we treat about conditions for which is possible to get C2,α estimates for solutions of second order, uniformly elliptic, fully non-linear equations: F(D2u,X) = f(X).Read More
Abstract: In this talk, we will discuss the characterization of do- mains maximizing the first non-zero Neuman eivgenvalue on a general cylinder. We will also present our study of overdeter- mined problem which arises from the Hadamard formula for this eigenvalue. A joint work with Tobias Weth.Read More