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Documents  35R11 | enregistrements trouvés : 4

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- 192 p.
ISBN 978-93-82006-17-6

Localisation : Colloque 1er étage (GORA)

fonctions spéciales # théorie de Lie # fonction de Bessel # fraction continue # polynôme de Jacobi # fonction hypergéométrique # algèbre de Racah-Wigner # transformation intégrale

33-XX ; 33Cxx ; 33E20 ; 33D60 ; 33D15 ; 35R11 ; 33C60 ; 33C45 ; 44-XX

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- ii; 105 p.

Localisation : Colloque 1er étage (JODH)

fonctions spéciales # intégrale de Kratzel # calcul fractionnel d'une fonction I # série hypergéométrique thêta # équation de Fokker-Planck # fonction hypergéométrique # expansion asymptotique # fonction W de Lambert

33E20 ; 33D60 ; 33D15 ; 35R11 ; 33C60 ; 33B20

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Research talks

The talk will review the motivations, state of the art, recent results, and open questions on four very related PDE models related to phase transitions: Allen-Cahn, Peierls-Nabarro, Minimal surfaces, and Nonlocal Minimal surfaces. We will focus on the study of stable solutions (critical points of the corresponding energy functionals with nonnegative second variation). We will discuss new nonlocal results on stable phase transitions, explaining why the stability assumption gives stronger information in presence of nonlocal interactions. We will also comment on the open problems and obstructions in trying to make the nonlocal estimates robust as the long-range (or nonlocal) interactions become short-range (or local). The talk will review the motivations, state of the art, recent results, and open questions on four very related PDE models related to phase transitions: Allen-Cahn, Peierls-Nabarro, Minimal surfaces, and Nonlocal Minimal surfaces. We will focus on the study of stable solutions (critical points of the corresponding energy functionals with nonnegative second variation). We will discuss new nonlocal results on stable phase transitions, explaining ...

82B26 ; 49Q05 ; 53A10 ; 35B35 ; 35R11

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Research talks

(Work in collaboration with C. Bardos and I. Moyano). Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse) reflection law with albedo coefficient $\alpha$. Moreover, assume that there is a temperature gradient on the boundary of the half-space, which radiates energy in the half-space according to the Stefan-Boltzmann law. In the asymptotic regime where $\sigma \to +\infty$ and $1 − \alpha ∼ C/\sigma$, we prove that the radiation pressure exerted on the boundary of the half-space is governed by a fractional diffusion equation. This result provides an example of fractional diffusion asymptotic limit of
a kinetic model which is based on the harmonic extension definition of $\sqrt{−\Delta}$. This fractional diffusion limit therefore differs from most of other such limits for kinetic models reported in the literature, which are based on specific properties of the equilibrium distributions (“heavy tails”) or of the scattering coefficient as in [U. Frisch-H. Frisch: Mon. Not. R. Astr. Not. 181 (1977), 273-280].
(Work in collaboration with C. Bardos and I. Moyano). Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse) reflection law with albedo coefficient $\alpha$. Moreover, assume that there is a temperature gradient on the boundary of the half-space, which radiates energy ...

45K05 ; 45M05 ; 35R11 ; 82C70 ; 85A25 ; 35Q20

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