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On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation.

On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation.

・ISBN 978-1-4704-3626-1 paper US$ 81.00

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お気に入り
著者・編者Collot, Charles / Raphael, Pierre / Szeftel, Jeremie,
シリーズMemoirs of the American Mathematical Society
出版社(American Mathematical Society, US)
出版年月2019
ページ数93 pp.
言語ENG
ニュース番号<M25-13781>

解説

The authors consider the energy super critical semilinear heat equation $\partial _{t}u=\Delta u u^{p}, x\in \mathbb{R}^3, p>5.$ The authors first revisit the construction of radially symmetric self similar solutions performed through an ode approach and propose a bifurcation type argument which allows for a sharp control of the spectrum of the corresponding linearized operator in suitable weighted spaces. They then show how the sole knowledge of this spectral gap in weighted spaces implies the finite codimensional nonradial stability of these solutions for smooth well localized initial data using energy bounds. The whole scheme draws a route map for the derivation of the existence and stability of self-similar blow up in nonradial energy super critical settings.