Advanced Partial Differential Equations  (Linear Equations)



M645 Introduction


Boundary Value Problems


1 Function Spaces

1a    The Mollifier Theorem

   2 Basic Facts About Hilbert Space

3 Fourier-Sobolev Spaces

4 Advanced Properties of Sobolev Spaces

   5 Intro to Distributions




6 Existence Proofs for Elliptic BVP's


7 H-Space Duality

8 Weak  formulation of Elliptic BVP's

            Problems on Weak Formulations

9 Spectral properties of Elliptic Operators


Evolution Equations


H valued Functions of t

Parabolic Equations

Hyperbolic Equations


Linear Operators

Intro to Semigroups

The Hille-Yosida theorem

The Lumer-Phillips theorem

Alternative Development of S/G's


Summary of Sg results


Analytic SemiGroups

Nonlinear IVP's