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On the stability of type I blow up for the energy super critical heat equation /
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 al...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
2019.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1255. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Chapter 1. Introduction; 1.1. Setting of the problem; 1.2. Type I and type II blow up; 1.3. Statement of the result; Acknowledgments; Notations; Organization of the paper; Chapter 2. Construction of self-similar profiles; 2.1. Exterior solutions; 2.2. Constructing interior self-similar solutions; 2.3. The matching; Chapter 3. Spectral gap in weighted norms; 3.1. Decomposition in spherical harmonics; 3.2. Linear ODE analysis; 3.3. Perturbative spectral analysis; 3.4. Proof of Proposition 3.1; Chapter 4. Dynamical control of the flow; 4.1. Setting of the bootstrap
- 4.2. ^{∞} bound4.3. Modulation equations; 4.4. Energy estimates with exponential weights; 4.5. Outer global ² bound; 4.6. Control of the critical norm; 4.7. Conclusion; 4.8. The Lipschitz dependence; Appendix A. Coercivity estimates; Appendix B. Proof of (4.43); Appendix C. Proof of Lemma 3.2; Appendix D. Proof of Lemma 3.3; Bibliography; Back Cover