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250134 VO Dispersive wave equations (2018S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Thursday 01.03. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 05.03. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 08.03. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 15.03. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 19.03. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 22.03. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 09.04. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 12.04. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 16.04. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 19.04. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 23.04. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 26.04. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 30.04. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 03.05. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 07.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 14.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 17.05. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 24.05. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 28.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Monday 04.06. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 07.06. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 11.06. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 14.06. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 18.06. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 21.06. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 25.06. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 28.06. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Dispersive equations are a very active area of research in the modern theory of partial differential equations with many crosslinks to physics. At least two Fields medals have been awarded for breakthrough contributions to dispersive PDEs and some of the strongest mathematicians worldwide are working in this field.
The course gives a gentle introduction to the theory of nonlinear dispersive wave equations. The main topics include basic well-posedness theory, tools from harmonic analysis (Calderon-Zygmund theory, Littlewood-Paley decomposition), Strichartz estimates, optimal local well-posedness, finite-time blowup, concentration-compactness techniques and stability theory. We will develop everything from scratch and the prerequisites are kept at a bare minimum. Nevertheless, we will make our way up to the forefront of current research.

Assessment and permitted materials

Oral exam.

Minimum requirements and assessment criteria

Ability to reproduce the main ideas and arguments developed in the course.

Examination topics

Everything covered in the lecture.

Reading list

I will not follow a particular reference but some books that might be useful are:
Tao: Nonlinear Dispersive Equations
Sogge: Lectures on Non-Linear Wave Equations
Rauch: Hyperbolic Equations and Geometric Optics
Kenig: Lectures on the Energy Critical Nonlinear Wave Equation
Muscalu, Schlag: Classical and Multilinear Harmonic Analysis
Grafakos: Classical Fourier Analysis, Modern Fourier Analysis
Stein, Shakarchi: Princeton Lectures in Analysis Part I, III, and IV

Association in the course directory

MANV

Last modified: Mo 07.09.2020 15:40