Séminaire Modélisation, Analyse et Calcul

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Organisateurs : Nicolas Godet, Grégory Faye & Ariane Trescases

Horaires et lieux habituels : mardi à 11h en amphi Schwartz (Bât. 1R3)

• Mardi 21 mai 11:00-12:00 - Workshop on variational problems in physics

Pas de séminaire pour cause de workshop

• Mardi 28 mai 11:00-12:00 - Fanny Delebecque - Institut de Mathématiques de Toulouse

TBA

Lieu : Amphi Schwartz

• Mardi 4 juin 11:00-12:00 - Lisl Weynans - Institut de Mathématiques de Bordeaux

Sharp cartesian methods for multifluid flows and electroporation of biological cells

Résumé : I will present numerical methods in the family of immersed boundary methods, designed to solve with elliptic problems with discontinuities across interfaces with complex shape.
The convergence of these methods will be studied using the framework of a discrete maximum principle and discrete Green functions, allowing to account for the various orders of the truncation errors.
These methods are applied to the simulation of flows with strong density ratios, as air-water interfaces, and also to the electropermeabilization of biological cells.

Lieu : Amphi L. Schwartz

• Mardi 11 juin 11:00-12:00 - Giampiero Palatucci - University of Parma

Hölder regularity for nonlocal double phase equations

Résumé : We present some regularity estimates for solutions to a class of possible degenerate and singular integro-differential equations whose leading operator switches between two different types of fractional elliptic phases, according to the zero set of a modulating coefficient $a=a(\cdot,\cdot)$. The model case is driven by the following nonlocal double phase operator,
$$\int \!\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}}\,{\rm d}y + \int \!a(x,y)\frac{|u(x)-u(y)|^{q-2}(u(x)-u(y))}{|x-y|^{n+tq}}\,{\rm d}y,$$ where $q\geq p$ and $a(\cdot,\cdot)\geqq 0$. Our results do also apply for inhomogeneous equations, for very general classes of measurable kernels. By simply assuming the boundedness of the modulating coefficient, we are able to prove that the solutions are Hölder continuous, whereas similar sharp results for the classical local case do require $a$ to be Hölder continuous. To our knowledge, this is the first result for nonlocal double phase problems.

Lieu : Salle MIP

• Mardi 18 juin 11:00-12:00 - Vianney Combet - Laboratoire Paul Painlevé, Université de Lille

TBA

Lieu : Amphi L. Schwartz

• Mardi 25 juin 08:30-12:30 -

Matinée d’équipe MIP

Lieu : Amphi L. Schwartz

• Mardi 10 septembre 11:00-12:00 - Caroline Japhet - Université Paris 13

Titre à préciser

Lieu : Amphithéâtre Laurent Schwartz

• Mardi 17 septembre 11:00-12:00 -

Pas de séminaire pour cause de conférence

• Mardi 24 septembre 11:00-12:00 - Christophe Lacave - Université Grenoble Alpes

TBA

Lieu : Amphithéâtre Laurent Schwartz

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