| Abstract: |
| In certain cosmological models (effective field theories) one
encounters a non-linear wave equation of the form
$$
u_{tt}=\alpha u_{xx} + \beta (u_x)^2
$$
with $\alpha>0$ and $\beta>0$ in $\ge 1$ dimension.
While cosmologists believed that solutions stay bounded for large
enough $\alpha$, it has been known for some time that nontrivial initial
conditions lead to divergence in finite time. After explaining some of
these results, I will focus also on the scaling of the diverging
solutions. (For the experts: In the cosmological context, one is not
allowed to scale the initial condition, since it is given by
background conditions.) |
|