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Softcover ISBN:  9781470436261 
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Softcover ISBN:  9781470436261 
Product Code:  MEMO/260/1255 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
eBook ISBN:  9781470453343 
Product Code:  MEMO/260/1255.E 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
Softcover ISBN:  9781470436261 
eBook ISBN:  9781470453343 
Product Code:  MEMO/260/1255.B 
List Price:  $162.00 $121.50 
MAA Member Price:  $145.80 $109.35 
AMS Member Price:  $97.20 $72.90 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 260; 2019; 93 ppMSC: Primary 35
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 selfsimilar blow up in nonradial energy super critical settings.

Table of Contents

Chapters

1. Introduction

2. Construction of selfsimilar profiles

3. Spectral gap in weighted norms

4. Dynamical control of the flow

A. Coercivity estimates

B. Proof of (4.43)

C. Proof of Lemma

D. Proof of Lemma


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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 selfsimilar blow up in nonradial energy super critical settings.

Chapters

1. Introduction

2. Construction of selfsimilar profiles

3. Spectral gap in weighted norms

4. Dynamical control of the flow

A. Coercivity estimates

B. Proof of (4.43)

C. Proof of Lemma

D. Proof of Lemma