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Third-Cycle Courses

Faculty of Engineering | Lund University

Details for Course FMA345F Dispersive Partial Differential Equations

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General
  • FMA345F
  • Temporary
Course Name
  • Dispersive Partial Differential Equations
Course Extent
  • 7.5
Type of Instruction
  • Third-cycle course
Administrative Information
  • 7151 (Centre of Mathematical Sciences / Mathematics)
  • 2026-01-15
  • /Jonas Johansson

Current Established Course Syllabus

General
  • English
  • If sufficient demand
  • Apply through e-mail
Aim
  • On completion of the course, participants shall be able to:

    Explain the dispersion phenomenon for linear dispersive equations.

    Understand and discuss main features of the two prototypical nonlinear dispersive PDEs: the Korteweg-de Vries and nonlinear Schrödinger equation.

    Identify problems that can be solved by methods that are part of the course
Contents
  • The course is an introduction to the concepts and analytical tools of nonlinear dispersive equations.
    We focus on existence theory and the long-time behavior of solutions. Prototypical examples such as the Korteweg–de Vries equation and the nonlinear Schrödinger equation will be discussed. We begin with the linear theory and examine how the dispersion relation influences the time decay of solutions. Incorporating nonlinear effects, we then turn to existence results and the long-term dynamics of solutions.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • Explain in depth the concepts, theorems and methods included in the course

    Understand and discuss main features of the Korteweg-de Vries and nonlinear Schrödinger equations.
Competences and Skills
  • For a passing grade the doctoral student must
  • Identify problems that can be solved by methods that are part of the course

    Describe the solution to a mathematical problem within the course framework, in speech and writing, logically coherent and with adequate terminology
Judgement and Approach
  • For a passing grade the doctoral student must
  • For a passing grade the student must be able to identify the applicability and limitation of the tools and concepts discussed in the course to related problems in partial differential equations.
Types of Instruction
  • Lectures
  • Seminars
Examination Formats
  • Seminars given by participants
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • The course participants are assumed to have basic knowledge in the theory of partial differential equations, Sobolev spaces, and Fourier transformation
Selection Criteria
Literature
  • Linares, F. & Ponce, G.: Introduktion till icke-linjära dispersive ekvationer. 2015. ISBN 9781493921805.
Further Information
Course code
  • FMA345F
Administrative Information
  • 2026-01-15
  • /Jonas Johansson

All Established Course Syllabi

1 course syllabus.

Valid from First hand in Second hand in Established
Spring 2026 2025‑12‑16 06:40:18 2025‑12‑17 11:48:44 2026‑01‑15

Current or Upcoming Published Course Occasion

No matching course occasion was found.

All Published Course Occasions

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0 course occasions.

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