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Product Code: | MEMO/260/1255.E |
List Price: | $81.00 |
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AMS Member Price: | $48.60 |
Softcover ISBN: | 978-1-4704-3626-1 |
eBook: ISBN: | 978-1-4704-5334-3 |
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Softcover ISBN: | 978-1-4704-3626-1 |
Product Code: | MEMO/260/1255 |
List Price: | $81.00 |
MAA Member Price: | $72.90 |
AMS Member Price: | $48.60 |
eBook ISBN: | 978-1-4704-5334-3 |
Product Code: | MEMO/260/1255.E |
List Price: | $81.00 |
MAA Member Price: | $72.90 |
AMS Member Price: | $48.60 |
Softcover ISBN: | 978-1-4704-3626-1 |
eBook ISBN: | 978-1-4704-5334-3 |
Product Code: | MEMO/260/1255.B |
List Price: | $162.00 $121.50 |
MAA Member Price: | $145.80 $109.35 |
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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 self-similar blow up in nonradial energy super critical settings.
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Table of Contents
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Chapters
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1. Introduction
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2. Construction of self-similar profiles
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3. Spectral gap in weighted norms
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4. Dynamical control of the flow
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A. Coercivity estimates
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B. Proof of (4.43)
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C. Proof of Lemma
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D. Proof of Lemma
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Additional Material
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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 self-similar blow up in nonradial energy super critical settings.
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Chapters
-
1. Introduction
-
2. Construction of self-similar 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