Advanced PDE

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Keywords

Advanced PDE

Objectives

This course will propose to study non-linear parabolic problems by the way of variational type techniques. A first approach of the type changing problems will be considered. The case of first order hyperbolic problems will be presented.

Recommended prerequisite

Prerequisites required:

Hilbert Analysis, Lebesgue and Sobolev spaces – functional analysis

Number of hours

  • CM : 27
  • TD : 12

Form of assessment

First session

Second session

Final assessment: 100%

Final assessment length: 3 hours

Remedial assessment: 100 %

Remedial assessment length: 3 hours

Syllabus

1) Vector valued distributions, spaces L^p(0,T,V) and W(0,T).

2) Non-degenerate parabolic problems: fixed-point theorems, time discretisation, and compactness.

3) Degenerate parabolic problems: artificial viscosity method.

4) First order hyperbolic problems in R, then in a bounded domain: characteristics method, notions of weak solution and entropy solutions.

5) First order hyperbolic problems in R^n: doubling variable method for uniqueness.

6) Existence via an artificial viscosity method.

Additional information

Bibliography:

Dautray Lions : Analyse mathématique et calcul numérique.

Brézis : Functional analysis.

Evans : Partial Differential Equations.

In brief

ECTS credits 4

Number of hours 39

Level of study Master degree level

Contact(s)

Organizational unit

Person in charge(s)

Vallet Guy

Email : guy.vallet @ univ-pau.fr

LEVI Laurent

Email : laurent.levi @ univ-pau.fr

Administrative contact(s)

Secrétariat de Mathématiques - Brigitte GAUBERT

Email : brigitte.gaubert @ univ-pau.fr

Places

  • Pau