RECENT PUBLICATIONS
My research is concentrated in the analytical and applied study of kinetic models. A central piece of it gravitates around Boltzmann type equations. The mathematical study of kinetic models involves numerous techniques based on functional, spectral and harmonic analysis of non linear and non local operators. Some of my most recent results involve the study of existence, uniqueness, and regularity for the Landau-Fermi-Dirac equation, Bose condensates stability for the quantum Boltzmann-condensation system, and the asymptotic dynamic of ballistic annihilation. Lately, I have been interested in the study of fractional diffusion scattering. In this direction some of my last papers discuss the radiative transfer equation with long-range interactions in bounded and unbounded domains, the non-cutoff Boltzmann equation, level set techniques (De’Giorgi arguments) for the analysis of regularity for the non-cutoff Boltzmann equation. I am also interested in studying the convergence of numerical methods for non local equations, for example see my paper on convergence and error estimates of the conservative spectral method for Boltzmann equation.
The .pdf of these papers and more can be found in my webpage:
https://www.researchgate.net/profile/Ricardo_Alonso2
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