Sumários

Energy method. Exercises.

10 Outubro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Uniqueness for the heat/diffusion equation, under various boundary conditions, by the energy method

Exercises on the Laplace equation.

The Laplace equation (part V). The Heat/Diffusion equation (part I)

8 Outubro 2019, 10:00 • Manuel Duque Pereira Monteiro Marques

The Laplace equation: Harnack's inequality.

The Heat/Diffusion equation: initial and boundary conditions, parabolic cylinder and parabolic boundary.
The weak maximum principle.

The Laplace equation (part IV)

4 Outubro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

The Poisson equation in a bounded domain.

Green's function and representation formula.
Green's function on a ball.

The Dirichlet principle. Exercises.

3 Outubro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Minimum problem associated to the classical BVP for the Poisson equation: the Dirichlet principle.

Comments and suggestions for the exercises of list 2.

The Laplace equation (part III)

1 Outubro 2019, 10:00 • Manuel Duque Pereira Monteiro Marques

Representation formulas. Fundamental solutions of the Laplace equation (outside the origin).

Representation formula for the solution of the Poisson equation in the whole space.
Behaviour at infinity and uniqueness of solution.