On the stability of type I blow up for the energy super critical heat equation
Author(s)
Bibliographic Information
On the stability of type I blow up for the energy super critical heat equation
（Memoirs of the American Mathematical Society, no. 1255）
American Mathematical Society, c2019
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"July 2019, volume 260, number 1255 (fourth of 5 numbers)"
Includes bibliographical reference
Description and Table of Contents
Description
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.
Table of Contents
Introduction
Construction of self-similar profiles
Spectral gap in weighted norms
Dynamical control of the flow
Appendix A. Coercivity estimates
Appendix B. Proof of (6.7)
Appendix C. Proof of Lemma 2.1
Appendix D. Proof of Lemma 2.2
Bibliography.
by "Nielsen BookData"