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