Partial Differential Equations in Analysis and Geometry
| Componente | Categoria |
|---|---|
| Andrea Drago | Dottorando/Assegnista/Specializzando componente non strutturato del gruppo di ricerca / PhD/Assegnista/Specializzando member non structured of the research group |
| Alessandro Savo | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Isabella Ianni | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Simone Dovetta | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Massimo Grossi | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Luigi Provenzano | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Fabio De Regibus | Dottorando/Assegnista/Specializzando componente non strutturato del gruppo di ricerca / PhD/Assegnista/Specializzando member non structured of the research group |
| Andrea Sambusetti | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Componente | Qualifica | Struttura | Categoria |
|---|---|---|---|
| Francesca Gladiali | Associate professor | Università di Sassari | Altro personale aggregato Sapienza o esterni, titolari di borse di studio di ricerca / Other aggregate personnel Sapienza or other institution, holders of research scholarships |
| Giusi Vaira | Associate professor | Università di Bari | Altro personale aggregato Sapienza o esterni, titolari di borse di studio di ricerca / Other aggregate personnel Sapienza or other institution, holders of research scholarships |
| Monica Clapp | Full professor | UNAM Mexico City | Altro personale aggregato Sapienza o esterni, titolari di borse di studio di ricerca / Other aggregate personnel Sapienza or other institution, holders of research scholarships |
| Bruno Colbois | Full professor | U. Neuchâtel (Switzerland) | Altro personale aggregato Sapienza o esterni, titolari di borse di studio di ricerca / Other aggregate personnel Sapienza or other institution, holders of research scholarships |
| Alberto Saldana | Associate professor | UNAM Mexico City | Altro personale aggregato Sapienza o esterni, titolari di borse di studio di ricerca / Other aggregate personnel Sapienza or other institution, holders of research scholarships |
| Gerard Besson | Full professor | U. Grenoble (France) | Altro personale aggregato Sapienza o esterni, titolari di borse di studio di ricerca / Other aggregate personnel Sapienza or other institution, holders of research scholarships |
We are interested in the effect of the nonlinearities on the emergence of non trivial patterns in several differential models arising in physics and other sciences. Such self organized structures correspond to selected solutions of the differential problem, possessing some special symmetries or shadowing particular shapes. We wish to understand the main analytical mechanisms involved in this process in terms of the common variational structure of the problems . A feature of this project rests indeed in the interchange of attack strategies between different specific applications in the fields of partial differential equations and systems. There is a remarkable unity in methodology across the different parts of the project. On the other hand, all the proposed issues must be addressed in interdisciplinary spirit and require expertise in several fields of mathematics: variational and topological methods, qualitative and regularity theory for partial differential equations and free boundary problems, Morse and critical point theory. We intend to address the following strongly interconnected themes:
(a) Pattern formation in reaction-diffusion systems and phase arising in multispecies and multiagent models.
(b) The effect of the geometry of the domain on the shape of the solutions to linear and nonlinear.
(c) Singular perturbation problems and concentration phenomena, as they appear in the study of partial differential equations and systems when, for some limiting values of a parameter, special solutions exhibiting a singular limiting behaviour appear.
This proposal aims at approaching all these different issues with the same basic methodology which relies on their common perturbative and/or variational structure. This requires expertise in different fields of mathematical analysis, Riemannian geometry and partial differential equations.