Modeling with partial differential equations

Lecture (online)

  • Wed, 8:45-10:15
  • Thu 9:00-10:30

The VO is read in blocks of 2 hours. Exact dates will be determined in the first lecture. A revision course will be offered Tue, 9-10. Zoom links can be found on TUWEL Kurs 101.500, opens an external URL in a new window.


Via Zoom, Tue 11-12
The zoom link is:

  • Meeting ID: 958 9773 3792
  • Passcode: 2q049f10


  • 1.10.2020: introduction to modelling
  • 7.10.2020: introduction to modelling: a traffic flow model, Burgers' equation, hyperbolicity, method of characteristics, notion of weak solution, Riemann problem
  • 8.10.2020: shock solution, Rankine-Hugoniot condition, rarefaction wave
  • 14.10.2020: Entropy conditions of Lax and Oleinik, viscosity solution
  • 15.10.2020: notion of entropy solution, Kruzkov's theorem
  • 21.10.2020: proof of Kruzkov's theorem, explicit solution of the traffic flow problem
  • 22.10.2020: shallow water equations
  • 28.10.2020: Introduction to continuum mechanics: Lagrangian and Eulerian coordinates, Reynolds' Transport Theorem
  • 29.10.2020: Proof of Reynolds' Transport Theorem, conservation of mass and momentum, Cauchy axiom
  • 4.11.2020: conservation of angular momentum, conservation of energy, some constitute equations (e.g., Fourier's law), concept of inviscid and viscous flow, Euler equations
  • 5.11.2020: some special cases of the Euler equations, in particular incompressible Euler equations, the assumptions underlying the NSE, Eriksen-Rivilin, incompressible NSE
  • 11.11.2020: Stokes flow, Reynolds number, Couette flow, Poiseuille flow
  • 12.11.2020: Potential flow, the principle of frame indifference
  • 17.11.2020: dimensional reduction, Buckingham Pi theorem
  • 18.11.2020: introduction to asymptotic expansions
  • 25.11.2020: the technique of matched asymptotics
  • 26.11.2020: Prandtl's boundary layer functions for the NSE
  • 2.12.2020: derivation of the KdV equation; two-timing
  • 3.12.2020: Introduction to elasticity equations, hyperelastic materials, principle of minimum potential energy
  • 9.12.2020: linear elasticity, 1.+2. Korn inequality
  • 11.12.2020: linear elasticity: variational formulations
  • 11.12.2020: linear elasticity: variational formulations, homogenization in 1D
  • 16.12.2020: homogenization in 2D, asymptotic expansions
  • 18.12.2020: variational inequalities, obstacle problem

Lecture Notes