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Course module: NWI-WM153
NWI-WM153
Nonlinear Wave Equations
Course infoSchedule
Course moduleNWI-WM153
Credits (ECTS)6
CategoryMA (Master)
Language of instructionEnglish
Offered byRadboud University Nijmegen; Faculty of Science; Wiskunde, Natuur- en Sterrenkunde;
Lecturer(s)
Coordinator
dr. D. Gajic
Other course modules lecturer
Lecturer
dr. D. Gajic
Other course modules lecturer
Contactperson for the course
dr. D. Gajic
Other course modules lecturer
Examiner
dr. D. Gajic
Other course modules lecturer
Academic year2021
Period
KW3-KW4  (31/01/2022 to 31/08/2022)
Starting block
KW3
Course mode
full-time
Remarks-
Registration using OSIRISYes
Course open to students from other facultiesYes
Pre-registrationNo
Waiting listNo
Placement procedure-
Aims
  • The student is aware of some important examples of nonlinear wave equations arising in mathematical physics.
  • The student understands how to prove the existence and uniqueness of solutions to the initial value problem for general linear wave equations.
  • The student is familiar with the local existence and uniqueness theory for semilinear wave equations.
  • The student is aware of some global existence and uniqueness results for semilinear and quasilinear wave equations.
  • The student understands how to work with energy estimates and the vector field method.
  • The students is comfortable working with Sobolev spaces, Sobolev inequalities, weak solutions etc. .
Content
Nonlinear wave equations form an important class of second-order partial differential equations and are abundant in science and engineering. In the context of Einstein's equations of general relativity, they play a fundamental role in determining the dynamical and geometric properties of space and time. They are also important for understanding nonlinear physical phenomena that arise in electromagnetism, fluid dynamics and acoustics. In this course, we will formulate the initial value problem for general nonlinear wave equations and we will derive existence and uniqueness of solutions. We will introduce the basic tools for understanding both local and global aspects of solutions, which include energy estimates and the vector field method. 

Instructional Modes
 
Level

Presumed foreknowledge
Analysis 1 and 2, basic knowledge of functional analysis.
Test information
Written exam (oral if the number participants is low) and assignments.
Specifics

Recommended materials
Book
ISBN:978-1-57146-279-4
Title:Lectures on Non-Linear Wave Equations
Author:C. Sogge
Edition:2
Book
ISBN:978-0821827499
Title:Geometric Wave Equations
Author:J. Shatal and M. Struwe
Book
ISBN:978-0821849743
Title:Partial Differential Equations
Author:L. Evans
Edition:2
Instructional modes
Course
Attendance MandatoryYes

Tests
Tentamen
Test weight1
OpportunitiesBlock KW4, Block KW4

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Kies de Nederlandse taal