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.

Exercise

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

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

Content

• 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

• Mr. Niklas Angleitner has created a summary of the lecture (PDF). Caveat: it has not been proofread by me.
• Mathematische Modellierung, C. Eck, H. Garcke, P. Knabner, Springer
• Parts of the lecture are based on the lecture notes (PDF) by Prof. Arnold
• interesting: the lecture notes of Christian Schmeiser (PDF)
• the lecture notes of A. Juengel

Übungsblätter

Handouts

• Details of the proof of Kruzkov's theorem (PDF) (I would be grateful for corrections)
• Remarks on Cauchy's axiom (PDF)
• Remarks on KdV equations (PDF)
• Comments on the transition Boltzmann to (compressible) Euler equations (PS)