This is an introductory class to the various types of evolution PDEs that arise from physical models. We present some of the mathematical techniques that can be used to solve those equations and to study the qualitative properties of the solutions. We emphasize perspective over technicalities and provide some references that cover each subject in greater detail for your own reading.
Skills that are required :
- General knowledge of functional analysis: minimal background in topology (norm and continuity), Banach and Hilbert spaces, Lebesgue’s integral, Lp spaces, Fourier on Rd and Td.
- Basic knowledge of ODEs (solve linear ODEs with constant coefficients in R and Rd, Cauchy- Lipschitz local well posedness theorem for non-linear equations).
- Basic proficiency in the theory of distributions: generalized functions D′(Rd) and S′(Rd).
Skills that you will acquire
- A sense of mathematical modelling of evolution phenomena.
- Overview of some fundamental methods to study ODEs and evolution PDEs.
- Some function spaces of general interest (Sobolev spaces, weak topology) and properties of some classical PDEs (examples studied in class).
- Technical proficiency, some bibliographic pointers and a general perspective that will allow you to learn more on your own in the rest of your doctoral studies.
