PARTIAL DIFFERENTIAL EQUATIONS II
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.
Books
- 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.
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Treves, J. E., Basic Linear Partial Differential Equations, Academic Press, 1975.