discipline

Pure Math

subject

Linear partial differential equations

lecturers

László Simon

credits

2

period

1.and 2. Semester, 2 hours/week

curriculum

1. semester:

Fourier transform of tempered distributions. Fundamental solutions of linear partial differential equations with constant coefficients. Sobolev spaces: extension operators, trace operator. Characterization of Sobolev spaces by Fourier transform. Smoothness of functions in Sobolev spaces.

Existence and uniqueness of weak solutions to boundary value problems for linear elliptic equations. Variational approach of boundary value problems and eigenvalue problems.

 

2. semester:

Elliptic boundary value problems with a parameter. Smoothness of the weak (variational) solutions of elliptic problems. Initial-boundary value problems for hyperbolic and parabolic equations: Fourier method, Galerkin method. Smoothness of solutions.

 

 

 

literature

R.E. Showalter: Hilbert space method for partial differential equations.

 

form of tuition

lectures

mode of assessment

oral exam