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We will study shock waves (i.e. a disturbance skirting regions with tremendously different properties e.g. of density, pressure, temperature) arising in systems of 1st order PDEs modeling e.g. transport phenomena, conservation laws, gas dynamics, wave equations, traffic flows. On this way, we will learn main notions and tools for the analysis of 1st order PDEs, in particular, characteristics, weak solutions, entropy, viscosity and asymptotics of solutions.
The language of the seminar is supposed to be English (with the help of German if needed).
Interested students are supposed to be acquainted with ordinary differential equations and analysis and should furthermore possess basic knowledge about partial differential equations.
Traveling waves arise in many fields of natural sciences, including biology, chemistry, and physics. We will learn mathematical tools that allow one to discribe the dynamics of traveling waves in reaction-diffusion systems. Besides classical systems, we will be interested in those containing time delay and spatially nonlocal interactions.
Knowledge of ordinary differential equations and/or dynamical systems is necessary. Basic understanding of partial differential equations will be helpful.