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- Universidad Autónoma de MadridES10 papers
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8 papers · 1 filter
Long-time dynamics of completely integrable Schrödinger flows on the torus
Nalini Anantharaman, Clotilde Fermanian-Kammerer, Fabricio Macià
In this article, we are concerned with long-time behaviour of solutions to a semi-classical Schrödinger-type equation on the torus. We consider time scales which go to infinity whe…
The forward problem for the electromagnetic Helmholtz equation with critical singularities
Juan Antonio Barceló, Luis Vega, Miren Zubeldia
We study the forward problem of the magnetic Schrödinger operator with potentials that have a strong singularity at the origin. We obtain new resolvent estimates and give some appl…
Classical solutions for a logarithmic fractional diffusion equation
Arturo de Pablo, Fernando Quirós, Ana Rodríguez +1
We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion posed…
A priori estimates for the Helmholtz equation with electromagnetic potentials in exterior domains
Juan Antonio Barceló, Luca Fanelli, Alberto Ruiz +1
We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension . We prove, by multiplier techniques in the sense of Mora…
A general fractional porous medium equation
Arturo de Pablo, Fernando Quirós, Ana Rodríguez +1
We develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion, $$ \{ll} \dfrac{\partial u}{\partial t} + (-Δ)^{σ/2} (|u|^{m-1}u…
Bivariate second--order linear partial differential equations and orthogonal polynomial solutions
I. Area, E. Godoy, A. Ronveaux +1
In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second--order linear partial diff…