In this event organised by Women in Mathematical Sciences at Lund, we have a guest speaker from the Karlsruhe Institute of Technology. Julia Henninger is a PhD student, and her research interests lie in non-linear partial differential equations. The talk will take place in MH:Hörmander in the MH building. Julia will tell us something about her research and about her career path, in a talk accessible for undergraduate students. Everybody is welcome and no registration is necessary for the talk. There will also be a get-together with the speaker after the talk. If you are interested in joining us for this get-together, please contact us at: women@math.lu.se

Title:  Special solutions to a semilinear wave equation 

Abstract: In this talk, we give an introduction into the field of semilinear wave equations and special solutions to it.
 

First, we present some applications of wave equations and study the  homogeneous wave equation in one dimension.
 

Next, we consider the wave equation in two dimensions with material dependent coefficients and introduce the notion of traveling waves. 

Lastly, we analyze the semilinear wave equation 
\begin{equation*}
    V(x)u_{tt} - u_{xx} = \Gamma(x) |u|^{p-1} u \text{ for } (x,t)\in\mathbb{R}^2 \label{eq:basic}
\end{equation*}
and look for solutions which are localized in space and periodic in time, so-called breathers, under suitable conditions on $V$ and $\Gamma$.