[Dottorcomp] Fwd: corso su Geometric PDEs di Ricardo Nochetto

[Luca Franco Pavarino]

---------- Forwarded message ---------
Da: Giancarlo Sangalli <giancarlo.sangalli a unipv.it>
Date: mar 29 nov 2022 alle ore 14:18
Subject: corso su Geometric PDEs di Ricardo Nochetto

tra i corsi brevi (3 CFU, 24h) della LM in matematica pavese,  nell'a.a.
22-23 sara` offerto il corso del prof. Ricardo H. Nochetto  che si terra` a
giugno, al Collegio Nuovo, e intitolato:

"Equazioni a derivate parziali geometriche: teoria e approssimazione"

Il corso fa parte del progetto "Collegiale non Residente",

http://news.unipv.it/wp-content/uploads/2022/06/2022_Brochure_collegiale-non-residente_web_v2.pdf

Il corso tratta argomenti a cavallo tra l'analisi funzionale, l'analisi
numerica, la geometria differenziale, e la fisica matematica (v. il
programma in calce).

A presto
Giancarlo

>
>
> ----------------------------------- programma del corso
 ------------------------------------
>
> Geometric Partial Differential Equations: Theory and Approximation
>
>
> 1. Introduction
>
>
>   Shape differential calculus: examples
>   Geometric gradient flows
>
> 2. Elements of Differential Geometry
>
>   Parametric surfaces: parametrizations, normal, area element
>   Tangential differential operators
>   Signed distance function
>   First and second fundamental forms
>   Divergence theorem on surfaces
>   The Laplace-Beltrami operator
>
> 3. Shape Differential Calculus
>
>   The velocity method
>   Material and shape derivatives
>   Shape derivatives of domain and contour integrals
>   Shape derivatives of geometric quantities
>   Shape derivatives of solutions of boundary value problems
>
> 4. Finite Element Methods for the Laplace-Beltrami Operator
>
>   Parametric FEM
>   Trace FEM
>   Narrow band FEM
>
> 5. Geometric Gradient Flows
>
>   Motivation: Allen-Cahn and Cahn-Hilliard models
>   Mean curvature flow
>   Optimal shape design
>   Surface diffusion
>   Willmore flow
>   Biomembranes: Helfrich flow
>
> 6. Gamma-Convergence
>
>   Definition
>   Convergence of absolute minimizers
>   Example: model reduction
>
> 7. Nonlinear Plate Theory
>
>   Nonlinear Kirchhoff model: large deformations and isometries
>   Bilayer plates
>   FEMs for bilayers
>   Gamma-convergence
>   Discrete gradient flow
>
> 8. Director Fields and Liquid Crystals
>
>   Approximation of director fields
>   Ericksen model for liquid crystals
>   Landau - de Gennes model for liquid crystals
>   Gamma-convergence
>   Discrete gradient flow
>
>
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