| Abstract: | We consider the heat equation in the half-line with
Dirichlet boundary data which blow up in finite time. Though the
blow-up set may be any interval 0,a],
a ? 0,￥]a\in0,\infty]
depending on the Dirichlet data, we prove that the
effective
blow-up set, that is, the set of points
x 3 0x\ge0
where the solution behaves like u(0,t), consists always only of the
origin.
As an application of our results we consider a system of two heat
equations with a nontrivial nonlinear flux coupling at the
boundary. We show that by prescribing the non-linearities the two
components may have different blow-up sets. However, the effective
blow-up sets do not depend on the coupling and coincide with the
origin for both components. |
