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Dettaglio Insegnamento

Context
Academic Year 2021/2022
Name Dott. - MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering
Programme Year 1

Course Details
ID Code 057409
Course Title REACTION-DIFFUSION 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 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.
Scientific-Disciplinary Sector (SSD) --

Details
Alphabetical group Professor Course details
From (included) To (excluded)
A ZZZZ Verzini Gianmaria, Soave Nicola
manifestidott v. 1.7.0 / 1.7.0
Area Servizi ICT
23/05/2022