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Higher order parabolic evolution equations have become a focus of interest in the last few years. In this talk we will discuss asymptotic and numerical approaches to investigate solutions to the Cauchy problem for the 6th order equation
\begin{equation}
u_t = \Delta^3 u - \Delta (|u|^{p-1}u)
\end{equation}
for various values of $p>0$. We will be primarily concerned with solutions that blow up in finite time, although some aspects of solutions that exist globally will also be addressed. |
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