EDP analysis 1

The construction of solutions to partial differential equations (PDEs) and the theoretical study of their qualitative behavior is essentially based on the use of analytical results, and in particular functional analysis. This course introduces the first important tools for solving PDEs from analytical or geometrical points of view. These tools will be put to use in the study of a few examples of PDEs representative of major classes of equations.

Introduce the basic tools for the theoretical study of classical linear PDEs in Rn.

Completion of undergraduate courses in measurement theory, integration and Fourier analysis;

Recommended prerequisites: The course will use the notions developed in the L1 and L2 UEs at the University of Montpellier on measure theory, integration and Fourier analysis of levels. The two L3 courses "Topologie des espaces métriques" and "Mesure, Intégration & Fourier" are also recommended.

An indicative course schedule is as follows.

• Additional measurement theory ("loc" spaces)
• Convolution product study 
• Distribution theory 
• Temperate distributions and Fourier transform.
• Sobolev spaces modelled on L2.

Hourly volumes :

            CM: 21h

            TD: 21h

            TP: 0

            Land: 0