
Dettaglio Insegnamento
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 
Codice Identificativo 
057409 
Denominazione Insegnamento 
REACTIONDIFFUSION 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 reactiondiffusion 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, AlexandroffBakelmanPucci in equality, Harnack inequality)
2. Semilinear boundary value problems: existence and multiplicity (sub and supersolutions, continuation and bifurcation, Mountain Pass lemma, critical point theory)
3. Qualitative theory (moving planes method, symmetry of positive solu tions, symmetry of stable solutions, apriori bounds and Liouvilletype 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, blowup, pattern formation. 
Settori Scientifico Disciplinari (SSD) 


Scaglione

Docente

Programma dettagliato

Da (compreso)

A (escluso)

A

ZZZZ

Verzini Gianmaria, Soave Nicola


