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:

  1. Evans, L. C., Partial Differential Equations, AMS, 1998.
  2. Kesavan, S., Topics in Functional Analysis and Applications, Wiley Eastern, 1988.
  3. Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983.
  4. Prasad, P. and Ravindran, R., Partial Differential Equations, Willey Eastern, 1985.
  5. Treves, J. E., Basic Linear Partial Differential Equations, Academic Press, 1975.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 11 Dec 2023