<div dir="ltr"><div class="gmail_quote"><div dir="ltr" class="gmail_attr">---------- Forwarded message ---------<br>Da: <strong class="gmail_sendername" dir="auto">Giancarlo Sangalli</strong> <span dir="auto"><<a href="mailto:giancarlo.sangalli@unipv.it">giancarlo.sangalli@unipv.it</a>></span><br>Date: mar 29 nov 2022 alle ore 14:18<br>Subject: corso su Geometric PDEs di Ricardo Nochetto</div>
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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:<br>
<br>
"Equazioni a derivate parziali geometriche: teoria e approssimazione"<br>
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Il corso fa parte del progetto "Collegiale non Residente",<br>
<br>
<a href="http://news.unipv.it/wp-content/uploads/2022/06/2022_Brochure_collegiale-non-residente_web_v2.pdf" rel="noreferrer" target="_blank">http://news.unipv.it/wp-content/uploads/2022/06/2022_Brochure_collegiale-non-residente_web_v2.pdf</a><br>
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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).<br><br>
A presto <br>
Giancarlo<br>
<br>
> <br>
> <br>
> ----------------------------------- programma del corso ------------------------------------<br>
> <br>
> Geometric Partial Differential Equations: Theory and Approximation<br>
> <br>
> <br>
> 1. Introduction<br>
> <br>
> <br>
> Shape differential calculus: examples<br>
> Geometric gradient flows<br>
> <br>
> 2. Elements of Differential Geometry<br>
> <br>
> Parametric surfaces: parametrizations, normal, area element<br>
> Tangential differential operators<br>
> Signed distance function<br>
> First and second fundamental forms<br>
> Divergence theorem on surfaces<br>
> The Laplace-Beltrami operator<br>
> <br>
> 3. Shape Differential Calculus<br>
> <br>
> The velocity method<br>
> Material and shape derivatives<br>
> Shape derivatives of domain and contour integrals<br>
> Shape derivatives of geometric quantities<br>
> Shape derivatives of solutions of boundary value problems<br>
> <br>
> 4. Finite Element Methods for the Laplace-Beltrami Operator<br>
> <br>
> Parametric FEM<br>
> Trace FEM<br>
> Narrow band FEM<br>
> <br>
> 5. Geometric Gradient Flows<br>
> <br>
> Motivation: Allen-Cahn and Cahn-Hilliard models<br>
> Mean curvature flow<br>
> Optimal shape design<br>
> Surface diffusion<br>
> Willmore flow<br>
> Biomembranes: Helfrich flow<br>
> <br>
> 6. Gamma-Convergence<br>
> <br>
> Definition<br>
> Convergence of absolute minimizers<br>
> Example: model reduction<br>
> <br>
> 7. Nonlinear Plate Theory<br>
> <br>
> Nonlinear Kirchhoff model: large deformations and isometries<br>
> Bilayer plates<br>
> FEMs for bilayers<br>
> Gamma-convergence<br>
> Discrete gradient flow<br>
> <br>
> 8. Director Fields and Liquid Crystals<br>
> <br>
> Approximation of director fields<br>
> Ericksen model for liquid crystals<br>
> Landau - de Gennes model for liquid crystals<br>
> Gamma-convergence<br>
> Discrete gradient flow<br>
> <br>
> <br>
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