Noticias en español
A characterization of well-posedness for abstract Cauchy problems with finite delay
In this talk, we characterize the mildly well-posedness of the first order abstract Cauchy problem with finite delay, solely in terms of a strongly continuous one-parameter family of bounded linear operators that satisfies a novel functional equation. In the case that the delay operator is null, this property is reduced to characterize the well-posedness of the first order abstract Cauchy problem in terms of the Abel’s functional equation that satisfies a C0- semigroup.
Read MoreA priori estimates for elliptic equations in $\mathbb R^N$ – a critical case
Abstract: Using the Moser’s iteraction method we obtain an a priori estimate for elliptic equations in whole euclidian space in a critical growth situation
Read MoreDynamics of strongly interacting unstable two-solitons for generalized Korteweg-de Vries equations.
Abstract. Many evolution PDEs admit special solutions, called solitons, whose shape does not change in time. A multi-soliton is a solution which is close to a superposition of a finite number K of solitons placed at a large distance from each other. I am interested in describing multi-soliton dynamics for generalized Korteweg-de Vries equations. I will present a general method of formally predicting the time evolution of the centers and velocities of each soliton. Then I will discuss in detail the case K = 2, in particular in the regime of strong interactions, which occurs when the...
Read MoreOn the 3D Ginzburg-Landau model of superconductivity
Abstract: The Ginzburg-Landau model is a phenomenological description of superconductivity. A crucial feature is the occurrence of vortices (similar to those in fluid mechanics, but quantized), which appear above a certain value of the applied magnetic field called the first critical field. We are interested in the regime of small ɛ, where ɛ>0 is the inverse of the Ginzburg-Landau parameter. In this regime, the vortices are at main order codimension 2 topological singularities. In this talk I will present a quantitative 3D vortex approximation construction for the Ginzburg-Landau...
Read MoreExistence of solutions to a pure critical elliptic system in a bounded domain
Abstract: http://capde.cl/past-seminars/
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