Determination of the curvature of the blow-up set and refined singular behavior for a semilinear

Continuity of the blow-up profile with respect to initial data and to the blow-up point for a semilinear heat equation.. Zaag d,

The goal of this paper is to investigate the role of the gradient term and of the diffusion coefficient in the preventing of the blow-up of the solution for semilinear and

– In Step 1, we derive from the stability of the blow-up behavior with respect to blow- up points in Im a a kind of weak differentiability of S at points of Im a (the cone property)..

C 1,α regularity of the blow-up curve at non characteristic points for the one dimensional semilinear wave equation. On the regularity of the blow-up set for semilinear

Indeed, the problem we are looking to is related to the so called existence and asymptotic stability of blow-up profile in the energy space (for L 2 critical generalized KdV, see

The wave equation has no new blow-up rate at the critical case, unlike NLS where new blow-up rates appear at the critical case (with respect to the conformal invariance), see Merle

In this paper, we adopt a global (in space) point of view, and aim at obtaining uniform estimates, with respect to initial data and to the blow-up points, which improve the results

We prove Theorem 1 in this subsection.. Therefore, if s is large enough, all points along this non degenerate direction satisfy the blow-up exclusion criterion of Proposition 2.3.