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Dettaglio Insegnamento

Contesto
Anno Accademico 2021/2022
Corso di Studi Dott. - MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering
Anno di Corso 1

Scheda Insegnamento
Codice Identificativo 057409
Denominazione Insegnamento REACTION-DIFFUSION EQUATIONS
Tipo Insegnamento MONODISCIPLINARE
Crediti Formativi Universitari (CFU) 5.0
Programma sintetico Semilinear elliptic equations and systems are of fundamental importance in several applied fields, such as physics, engineering and life sciences. They are stationary partial differential equations, which appear in different contexts: for instance, when searching for equilibrium solutions to the corresponding evolution equations, for traveling wave solutions to reaction-diffusion equations, for solitary wave solutions in quantum mechanics (Schroedinger equations). This course aims to provide a basic introduction to the analytical study of such equations, starting from the linear case, whose prototype is the Poisson equation. The main topics will include: 1. Weak solutions of linear elliptic equations (existence, qualitative prop- erties, eigenvalues, maximum principle, Alexandroff-Bakelman-Pucci in- equality, Harnack inequality) 2. Semilinear boundary value problems: existence and multiplicity (sub- and super-solutions, continuation and bifurcation, Mountain Pass lemma, critical point theory) 3. Qualitative theory (moving planes method, symmetry of positive solu- tions, symmetry of stable solutions, a-priori bounds and Liouville-type theorems) 4. The Nehari manifold (and applications to the existence of ground state solutions for the nonlinear Schrodinger equations and systems). 5. Dynamical issues: stability, blow-up, pattern formation.
Settori Scientifico Disciplinari (SSD) --

Dettaglio
Scaglione Docente Programma dettagliato
Da (compreso) A (escluso)
A ZZZZ Verzini Gianmaria, Soave Nicola
manifestidott v. 1.7.0 / 1.7.0
Area Servizi ICT
12/08/2022