MA 342: Partial Differential Equations II
Credits: 3:0
Introduction to distribution theory and Sobolev spaces, Fundamental solutions for Laplace, heat and wave operations.
Second order elliptic equations: Boundary value problems, Regularity of weak solutions, Maximum principle, Eigenvalues.
Semi group theory:Hille-Yosida theorem, Applications to heat, Schroedinger and wave equations.
System of first order hyperbolic equations: Bicharacteristics, Shocks, Ray theory, symmetric hyperbolic systems.
Suggested books and references:
- Evans, L. C., Partial Differential Equations, AMS, 1998.
- Kesavan, S., Topics in Functional Analysis and Applications, Wiley Eastern, 1988.
- Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983.
- Prasad, P. and Ravindran, R., Partial Differential Equations, Willey Eastern, 1985.
- Treves, J. E., Basic Linear Partial Differential Equations, Academic Press, 1975.