Two Courses on Applications of Complex Analysis

Departamento de Matemática, Universidade de Coimbra

  9-16 March 2001

With support from CMUC (Centro de Matemática da Universidade de Coimbra)and Socrates programme

Table of contents

Schedule of the course

Abstracts

Author: Jan de Graaf

Title: PDE Reducing the Stokes equations in dimensions 2 and 3 to an integral equation at the boundary.

Abstract:

1. Review of the Dirichlet and Neumann boundary value problem for the Poisson equation on arbitrary domains. Illustration with geometrically simple cases.
2. Introduction of Stokes' equations. General solutions of it in 2 and 3 dimensions.
3. Introduction of the operator equation at the boundary' for solving Stokes' equations with prescribed velocities at the boundary of an arbitrary domain.
4. Theory of solving the mentioned operator equations applying spaces of harmonic functions.
5. Explicit solutions on (semi-)strips, wedges, balls... The latter in terms of spherical harmonics. If time is left: Non-linear boundary conditions.

• J. Carvalho e Silva (Departamento de Matemática Universidade de Coimbra)

• Amilcar Branquinho (Departamento de Matemática Universidade de Coimbra) 

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