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Equazioni Differenziali non Lineari

academic year:	2013/2014
instructors:	Filomena Pacella, Antonio Siconolfi
degree courses:	Mathematics (magistrale) Mathematics for applications (magistrale)
credits:	6 (48 class hours)
scientific sector:	MAT/05 Analisi Matematica
teaching language:	italiano
period:	I sem (30/09/2013 - 17/01/2014)

Lecture meeting time and location

Presence: highly recommended

Module subject: - Symmetry theorems for solutions of semilinear elliptic equations -Uniqueness of positive solutions of semilinear partial differential equations of elliptic type -Global existence and blow up in finite time of solutions of nonlinear parabolic equations - Viscosity solutions for I and II order equations - Regularization by sup and inf convolutions - Existence, comparison and stability theorems. Representation of solutions - Homogenization of Hamilton-Jacobi equations.

Suggested readings:

H.Brezis : Functional Analysis, Sobolev Spaces and Partial Differential Equations , Springer
M. Bardi, I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems & Control: Foundations & Applications. Birkhäuser Boston, Inc., Boston, MA, 1997.
Recent papers on the topics of the course

Issues:

Type of course: standard

Prerequisites: Analisi Reale, Istitituzioni di Analisi Superiore

Knowledge and understanding:
It is the purpose of the course to present advanced tools and results to study some classes of nonlinear partial differential equations.

Skills and attributes:
After taking the exam, the student will be able to address an advanced study of classical and generalized solutions for some classes of nonlinear partial differential equations.

Personal study: the percentage of personal study required by this course is the 65% of the total.

Examination dates on Infostud

Statistical data on examinations