Threshold and generic type I behaviors for a supercritical nonlinear heat equation
By Hiroshi Matano, F. Merle. 2011
66 citations recorded by the source corpus.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e14979027cea3576c6b00d32c276010132dd01cd
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Thomas Duyckaerts
- Carlos E. Kenig
- Monica Musso
- Manuel del Pino
- F. Merle
- Pavol Quittner
- Charles Collot
- Raphael Cote
In Mathematical Physics
- Carlos E. Kenig
- Thomas Duyckaerts
- F. Merle
- Monica Musso
- Manuel del Pino
- Charles Collot
- Raphael Cote
- B. Dodson
Citations in the corpus
- Classification of radial solutions of the focusing, energy-critical wave equation (2012, methodology): “We believe that one could deduce from Theorem 1, using arguments similar to the ones in [30] for the radial heat equation or in [35] for the L2-critical nonlinear Schrödinger equation, that S3 is the boundary of S1 ∪ S2.”
- Nonradial type II blow up for the energy-supercritical semilinear heat equation (2016, result): “The result generalizes previous works on the existence of type II blow-up solutions, either constructive [14, 15, 35] or nonconstructive [25, 36], which only existed in the radial setting and relied on parabolic arguments.”
- Green's function and infinite-time bubbling in the critical nonlinear heat equation (2016, background): “In particular, the role of the Sobolev critical exponent p = n+2 n−2 in existence and characteristics of blow-up phenomena has been broadly considered, see also Matano and Merle [18] for a more recent classification of radial blow-up and supercritical powers and Schweyer [23] for a construction of r”
- 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.”
- Optimal Liouville theorems for superlinear parabolic problems (2020, background): “arguments in [12] and proved in [30, 7, 8, 9, 17, 18]. Type II blow-up can also occur for positive radial and non-radial solutions if n ≥ 11 and p ≥ pJL, where pJL := 1+4 n−4+2 √ n−1 (n−2)(n−10) (see [19, 20, 3, 4, 31]). In the case of smooth domains and Dirichlet boundary conditions, Theorem 1 impl”