We assume that the conditions (1.7) hold (as in the blow-up case [11]).
The inset in panel (a) is a blow-up of the first peak in the trace of panel (a).
A local linear stability analysis shows that this regularization successfully penalises the short wavelength growth which is usually associated with blow-up [13].
We are not in this paper primarily concerned with blow-up, but rather with the underlying mathematical structure of the free boundary problems.
This would lead to gradient blow-up of the solution of the graph equation.
This estimate corresponds to the asymptotic analysis of blow-up patterns we are going to perform in the next sections.
Total wave collapse will take place provided the blow-up singularity does not occur at times earlier than the collapse predicted by the virial theorem.
As for the solid fuel model (1.1), the structure of such a blow-up singularity formation is of importance in the present higher-order model.
