ABSTRACT
We have seen above that, in general, blow-up occurs for some initial data, since, in many cases, small data can lead to globally existing sufficiently small solutions (of course, if 0 has a nontrivial stable manifold). Below, we introduce classes of such “blow-up data,” i.e., initial functions
generating finite-time blow-up of solutions. Actually, studying such crucial data will eventually require the performance of a detailed study of the corresponding elliptic systems with non-Lipschitz nonlinearities.
