PDE analysis 1

The construction of solutions of partial differential equations (PDEs) and the theoretical study of their qualitative behavior is essentially based on the use of analytical results and in particular of functional analysis. This course presents the first important tools for the solution of PDEs via analytical or geometrical points of view. These tools will be implemented in the study of some examples of PDEs representative of large classes of equations.

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

Completed courses in measurement theory, integration and Fourier analysis at the undergraduate level;

Recommended prerequisites: The course will use the notions developed in the L1 and L2 courses at the University of Montpellier on measure theory, integration and Fourier analysis of levels. The two L3 courses "Topology of metric spaces" and "Measure, Integration & Fourier" are also recommended.

An indicative program of courses is as follows.

• Complements of measure theory (the "loc" spaces)
• Study of the Convolution product 
• Notions on the theory of distributions 
• Temperate distributions and Fourier transform.
• Sobolev spaces modeled on L2.

Hourly volumes:

            CM : 21h

            TD : 21h

            TP : 0

            Land : 0