Evolution Equations
- Professors:
- Rocca Elisabetta, Veneroni Marco
- Year:
- 2015/2016
- Course code:
- 500699
- ECTS:
- 6
- SSD:
- MAT/05
- DM:
- 270/04
- Lessons:
- 56
- Period:
- II semester
Objectives
This course will provide the fundamental concepts required to deal with evolution equations, as well as insight into some recent developments.
Teaching methods
Lectures and exercise sessions
Examination
Oral exam
Prerequisites
Basic concepts of functional analysis, Lebesgue integration theory and Sobolev spaces (the main results will be recalled during the course).
Syllabus
-Functions in Banach spaces, Bochner integral, vector-valued Lebesgue and Sobolev spaces, absolutely continuous functions.
-Lions method and forms: Hilbert triple, bilinear forms, Lions theorem, existence uniqueness and continuous dependence from initial data.
-Applications to evolution equations: well-posed Cauchy problem for first order (in time) equations: heat equation, reaction-diffusion equations.
-Gradient flows: Classical theory in Hilbert spaces, (an introduction to) the Wasserstein approach, discretization via minimizing movements, an application: the Fokker-Planck equation and a simple reaction-diffusion equation.
-Lions method and forms: Hilbert triple, bilinear forms, Lions theorem, existence uniqueness and continuous dependence from initial data.
-Applications to evolution equations: well-posed Cauchy problem for first order (in time) equations: heat equation, reaction-diffusion equations.
-Gradient flows: Classical theory in Hilbert spaces, (an introduction to) the Wasserstein approach, discretization via minimizing movements, an application: the Fokker-Planck equation and a simple reaction-diffusion equation.
Bibliography
H. Brezis, Functional analysis, Sobolev spaces and Partial differential equations, Springer 2010.
H. Brezis, Op?rateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Publishing Co., Amsterdam 1973.
Lecture notes and research articles.
H. Brezis, Op?rateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Publishing Co., Amsterdam 1973.
Lecture notes and research articles.
Modules
- Professor:
- Rocca Elisabetta
- Lessons:
- 28
- ECTS:
- 3
- SSD:
- MAT/05
- Professor:
- Veneroni Marco
- Lessons:
- 28
- ECTS:
- 3
- SSD:
- MAT/05
Dipartimento di Matematica ''F. Casorati''
Università degli Studi di Pavia -
Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602