Partial Differential Equations III (A)

Spring Term 1997/98

Master's degreee in Applied Mathematics


Strongly Continuous Semigroups of Bounded Linear Operators.
The Hille-Yosida theorem. The Lumer-Phillips theorem. Stone's theorem. The Abstract Cauchy Problem. Applications, including a wave equation and a Shrödinger equation.

Nonvariational Techniques for Nonlinear PDE's.
Monotonicity Methods. Schauder's and Shaefer's fixed point theorems. Subsolutions and Supersolutions. Pohozaev's identity. Geometric properties of solutions. The Gidas, Ni, Nirenberg theorem (bounded and unbounded domains). Brouwer degree. Leray-Schauder degree. Applications.


2º Semestre de 2003/04