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Workgroup Nonlinear Partial Differential Equations

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 3.029

Address
Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe
Germany

Office hours:
Mon-Fri 10-12, Tue+Wed 14-16

Tel.: +49 721 608 42064

Fax.: +49 721 608 46530

Photo of Dominic Scheider M.Sc. Dominic Scheider

Office hour for students: on appointment
Room: -1.021 Kollegiengebäude Mathematik (20.30)
Tel.: 0049 721 608 42046
Fax.: 0049 608 46530
Email: dominic.scheider@kit.edu

Englerstraße 2
76131 Karlsruhe





Current List of Courses
Semester Titel Typ
Winter Semester 2019/20 Proseminar
Summer Semester 2019 Seminar
Winter Semester 2018/19 Seminar
Summer Semester 2018 Proseminar
Winter Semester 2017/18 Lecture
Summer Semester 2017 Lecture
Proseminar


Research

In my PhD project, I analyse systems of two coupled nonlinear Helmholtz equations such as

$  - \Delta u - \mu u = u \: (u^2 + b \: v^2) \quad\text{in }\mathbb{R}^3, \qquad - \Delta v - \nu v = v \: (v^2 + b \: u^2) \quad\text{in }\mathbb{R}^3, 
 \qquad  u, v \in L^4(\mathbb{R}^3)   $

where  \mu, \nu > 0 and  b denotes a (constant or periodic) coupling.
The goal is to prove the existence of solutions using tools from, e.g., variational calculus or bifurcation theory.

Why the Helmholtz equation? It is a fundamental equation in physics describing the propagation and scattering of waves.
For more information, please visit the webpage of our research group.


Publications and Preprints

R. Mandel, D. Scheider: Dual Variational Methods for a Nonlinear Helmholtz System. NoDEA Nonlinear Differential Equations Appl. 25 (2018), no. 2, 25:13.

R. Mandel, D. Scheider: Bifurcations of nontrivial solutions of a cubic Helmholtz system. (2018, Preprint).





Teaching: Special help for starters

For further teaching activities concerning the "special help for starters" offered by the Departement of Mathematics, please visit the German webpage.