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, 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.
+91 (80) 2293 2711, +91 (80) 2293 2265 ; E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 05 Dec 2019