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An introduction to PDEs

Course Type: 
PhD Course
Academic Year: 
2014-2015
Period: 
October-January
Duration: 
50 h
Description: 
  • Introduction to partial differential equations (PDEs).
  • Linear wave and Schroedinger equation, linear transport and heat equation, Laplace and Poisson equation: fundamental solutions and representation formulas.
  • Harmonic functions, maximum principle, analiticity, Green's functions.
  • Periodic boundary conditions: resolution by Fourier series.
  • Equations on R^n: resolution by Fourier transform.
  • Dispersive equations.
  • Energy estimates.
  • Some existence and unicity results concerning the initial value problem of nonlinear PDEs of evolution type, like the Schroedinger equation.
Location: 
A-133

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