On Nonexistence of type II blowup for a supercritical nonlinear heat equation

By Hiroshi Matano, F. Merle. 2004

189 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c6530e03959458c10ca51e9697b5e02c36b603a3

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Proof of a Spectral Property related to the singularity formation for the L2 critical nonlinear Schrödinger equation (2006, background): “A typical striking example is for the supercritical nonlinear heat equation u t = u + u p , where, for p large and N ≥ 11, a new blow up regime appears; see Matano and Merle [12].”
Nonradial type II blow up for the energy-supercritical semilinear heat equation (2016, background): “First, the assumption p > pJL is not just technical as radial type II blow-up is impossible for d+2 d−2 < p < pJL [23, 39].”
On Blow up at Space Infinity for Semilinear Heat Equations (2006, background): “If one considers only radial solution of (1) for supercritical p less than 1 + 4/(n− 4− 2(n− 1)) or n ≤ 10, then the estimate (5) holds [11].”
Threshold and generic type I behaviors for a supercritical nonlinear heat equation (2011, background): “Before concluding this section, we remark that the following proposition can easily be derived from our earlier results found in [17, 18].”
Profile for a Simultaneously Blowing up Solution to a Complex Valued Semilinear Heat Equation (2013, result): “oﬁle with respect to initial data has been proved by Fermanian Kammerer, Merle and Zaag in [FKZ00] and [FKMZ00]. For more results on equation (3), see [Bal77], [GK85], [GK87], [GK89], [HV93], [HV94], [MM04], [MM09], [MZ98], [MZ00], [Miz07] and [QS07]. 2 As we inferred above, equation (1) appears as ”
Infinite-time blow-up for the 3-dimensional energy-critical heat equation (2017, unknown): “We refer the reader for instance to the book [32] for background and a comprehensive account of results until 2007 and to the more recent works [21, 22, 23] and references therein.”
Blow-up profile for the complex Ginzburg–Landau equation (2008, background): “As a matter of fact, in the case of the pure heat equation β = δ = 0 and (N − 2)p N + 2, such a classification was done (in the form of a Liouville Theorem) by Merle and Zaag in [15] and [16] (see also Nouaili [17]), yielding uniform estimates for blow-up solutions.”