Classification of Partial Differential Equations, Cauchy Problem, Cauchy Kowalevski Theorem, Lagrange-Green identity, The uniquness theorem of Holmgren,
Transport equation: Initial value problem, nonhomogeneous problem
Laplace equation: Fundamental solution, Mean Value formula, properties of Harmonic functions, Green’s function, Energy methods, Harnack’s inequality.
Heat Equation: Fundamental solution, Mean value formula, properties of solutions.
Wave equation: Solution by spherical means, Nonhomogeneous problem, properties of solutions.
- L. C. Evans, “Partial Differential Equations”, Graduate Studies in Mathematics 19, American Mathematical Society, 2010.
- F. John, “Partial Differential Equations”, Springer International Edition, 2009.
- G. B. Folland, “Introduction to Partial Differential Equations”, Princeton University Press, 1995.
- S. Kesavan, “Topics in Functional Analysis and Applications”, John Wiley & Sons, 1989.