slideshow 3

Seminar on Partial Differential Equations

usually takes place each Tuesday at 09:00 in IM, rear building, ground floor
Chair: Šárka Nečasová, Milan Pokorný

On Preisach operators and piezoelectricity modeling

Giselle Monteiro
Institute of Mathematics, CAS
Tuesday, 11. December 2018 - 9:00 to 10:00
Preisach operators are rate independent hysteresis operators capable of reproducing minor loops, therefore they are well fitted to measurements of smart materials. Benefiting from this observation, some authors have proposed models for piezoelectricity assuming that all hysteresis effects are due to one single Preisach operator. More accurate models though have to account thermal effects. To address this problem, we introduce a notion of parameter-dependent Preisach operator and investigate some properties of its inverse.
This is a joint work with P. Krejci.

Unilateral sources of an activator in reaction-diffusion systems describing Turing’s patterns

Martin Fencl
University of West Bohemia, Pilsen
Tuesday, 4. December 2018 - 10:00 to 11:00
See the attachment.

Wild solutions for isentropic Euler equations starting from smooth initial data

Ondřej Kreml
Institute of Mathematics, CAS
Tuesday, 27. November 2018 - 9:00 to 10:00
In a series of papers starting with the groundbreaking work of De Lellis and Székelyhidi several authors have shown that there might exist infinitely many bounded weak solutions to the isentropic Euler equations satisfying the energy inequality and starting from certain class of initial data. Concerning smoothness, the best result is due to Chiodaroli, De Lellis and Kreml, where the existence of these wild solutions was shown for Lipschitz initial data. In this talk we present the same result for smooth initial data. The proof is based on a nontrivial generalization of the previous theorem, in particular on a notion of generalized fan subsolution.
This is a joint work with E. Chiodaroli, V. Mácha and S. Schwarzacher.

Homogenization in the presence of defects

Xavier Blanc
Université Paris-Diderot
Tuesday, 20. November 2018 - 9:00 to 10:00
We will present some results on homogenization for linear elliptic equation. The geometry will be assumed to be either a perturbation of a periodic background, or an interface between two periodic media. In both cases, we study the homogenization problem, prove existence of a corrector, and use to build a two-scale expansion of the solution. We prove convergence estimates of this two-scale expansion.
These are a joint works with C. Le Bris (Ecole des Ponts, Paris), P.-L. Lions (Collège de France, Paris) and M. Josien (Ecole des Ponts, Paris).