Valutami
Scheda programma d'esame
EQUAZIONI ALLE DERIVATE PARZIALI
VIERI BENCI
Anno accademico2016/17
CdSMATEMATICA
Codice545AA
CFU6
PeriodoPrimo semestre
LinguaItaliano

ModuliSettore/iTipoOreDocente/i
EQUAZIONI ALLE DERIVATE PARZIALIMAT/05LEZIONI48
VIERI BENCI unimap
Programma non disponibile nella lingua selezionata
Learning outcomes
Knowledge
The student who successfully completes the course should acquire a good knowledge on the basic facts and the main methods of the theory of PDE's, especially those coming from physical problems including transport equations, Laplacian, vibrating string, wave equations, heat equation, Schroedinger equation, Friedrichs symmetric systems.
Assessment criteria of knowledge

Methods:

  • Final oral exam
  • Oral report

Further information:
The exam will consist firstly in a seminar presentation on a subject chosen by the candidate in accord the teacher, and then in a discussion on some main topics of the course.

Teaching methods

Delivery: face to face

Learning activities:

  • attending lectures
  • preparation of oral/written report
  • participation in discussions
  • individual study
  • Bibliography search

Attendance: Advised

Teaching methods:

  • Lectures
Syllabus
Recalls on Lebesgue Integral and Banach-Hilbert spaces. L^p spaces. Weak derivatives and Sobolev spaces. Fourier transform. Paley-Wiener theorem. Mollifiers. Dirac delta measure . Distributions. First order transport equations and characteristic curves. D'Alembert formula for String equation. Fundamental solution for Heat equation. Kirchhoff formula for Wave equation. Finite speed of propagation and Huygens principle. Hadamard well-posedness and hyperbolicity. Energy method for symmetric systems. Strictly hyperbolic systems
Bibliography
L. Evans, Partial Differential Equations, Graduate Studies Math. 19, Am. Math. Soc. 1998 S. Salsa, Equazioni a Derivare Parziali. Metodi, modelli, applicazioni, Springer 2010 S. Spagnolo, Appunti del corso
Ultimo aggiornamento 14/11/2016 17:27