MA 342: 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
System of first order hyperbolic equations: Bicharacteristics, Shocks, Ray
theory, symmetric hyperbolic systems.
Suggested books and references:
Evans, L. C., Partial Differential Equations
Kesavan, S., Topics in Functional Analysis and Applications
,Wiley Eastern, 1988.
Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations
Prasad, P. and Ravindran, R., Partial Differential Equations
,Willey Eastern, 1985.
Treves, J. E., Basic Linear Partial Differential Equations
,Academic Press, 1975.
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