
Dettaglio Insegnamento
Academic Year 
2021/2022 
Name 
Dott.  MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering 
Programme Year 
1 
ID Code 
057409 
Course Title 
REACTIONDIFFUSION EQUATIONS 
Course Type 
MONODISCIPLINARE 
Credits (CFU / ECTS) 
5.0 
Course Description 
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. 
ScientificDisciplinary Sector (SSD)



Alphabetical group

Professor

Course details

From (included)

To (excluded)

A

ZZZZ

Verzini Gianmaria, Soave Nicola


