The course introduces the study of partial differential equations (PDE). Given the richness and the variety of physical, geometric and probabilistic phenomena that these equations can describe, there is no general theory that allows them to be studied and solved in a unified way. We therefore aim to analyze equations and methods that are the most important for applications. Large attention will be given to some specific linear PDEs of the first and second order (linear transport equation, Laplace and Poisson equations, heat equation, wave equation); hints of theory for some non-linear PDEs will also be provided.
The aim of this course is to provide a first introduction to the theory of partial differential equations.
Learn to classify partial differential equations and identify the most appropriate resolution or analysis methods for each of the "classical" ones; know how to apply them to find formulas for representing solutions or to establish their qualitative properties.
A basic knowledge of measure theory, Lebesgue spaces and ordinary differential equations is recommended.
Traditional teaching (theoretical lessons on the blackboard and exercises)
Linear transport equation, Laplace and Poisson equations, harmonic functions, Perron method, heat equation, wave equation, method of characteristics, conservation laws, other methods for representing solutions.
Evans, "Partial Differential Equations"
Salsa, "Equazioni a derivate parziali"
Ricevimento: By appointment
FLAVIANA IURLANO (President)
SIMONE DI MARINO
FILIPPO DE MARI CASARETO DAL VERME (President Substitute)
ANDREA BRUNO CARBONARO (Substitute)
MATTEO SANTACESARIA (Substitute)
Classes begin October 2, 2023
Written and oral exam
The written exam will verify:
The oral exam will verify:
