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Type II Blow up Solutions with Optimal Stability Properties for the Critical Focussing Nonlinear Wave Equation on {R}^{3+1}
| Type II Blow up Solutions with Optimal Stability Properties for the Critical Focussing Nonlinear Wave Equation on {R}^{3+1} |
| Autore | Burzio Stefano |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2022 |
| Descrizione fisica | 1 online resource (88 pages) |
| Disciplina |
515/.353
515.353 |
| Altri autori (Persone) | KriegerJoachim |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Nonlinear wave equations
Blowing up (Algebraic geometry) Perturbation (Mathematics) Asymptotic expansions Iterative methods (Mathematics) Fourier transformations Partial differential equations -- Hyperbolic equations and systems -- Wave equation Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions |
| ISBN |
9781470471699
1470471698 |
| Classificazione | 35L0535B40 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Cover -- Title page -- Chapter 1. Introduction -- 1.1. The type II blow up solutions of [33], [32] -- 1.2. The effect of symmetries on the solutions of Theorem 1.1 -- 1.3. Conditional stability of type II solutions -- 1.4. Spectral theory associated with the linearisation ℒ -- 1.5. Description of the data perturbation in terms of the distorted Fourier transform -- 1.6. Outline of the main result from [26] -- 1.7. Figures -- Chapter 2. The main theorem and outline of the proof -- 2.1. The main theorem -- 2.2. Outline of the proof -- Chapter 3. Construction of a two parameter family of approximate blow up solutions -- 3.1. Step 0: the bulk term -- 3.2. Step 1: choice of the first correction ₁ -- 3.3. Step 2: the ₁ error -- 3.4. Step 3: choice of second correction ₂ -- 3.5. Step 4: the ₂ error -- 3.6. Step 5: inductive step -- 3.7. Step 6: choice of _{ ℎ, }, =1,2 -- Chapter 4. Modulation theory -- determination of the parameters _{1,2}. -- 4.1. Re-scalings and the distorted Fourier transform -- 4.2. The effect of scaling the bulk part -- Chapter 5. Iterative construction of blow up solution almost matching the perturbed initial data -- 5.1. Formulation of the perturbation problem on Fourier side -- 5.2. The proof of Theorem 5.1 -- 5.3. Translation to original coordinate system -- Chapter 6. Proof of Theorem 2.1 -- Chapter 7. Outlook -- Bibliography -- Index -- Back Cover. |
| Record Nr. | UNINA-9911091400703321 |
Burzio Stefano
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| Providence : , : American Mathematical Society, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Type II Blow up Solutions with Optimal Stability Properties for the Critical Focussing Nonlinear Wave Equation on {R}^{3+1}
| Type II Blow up Solutions with Optimal Stability Properties for the Critical Focussing Nonlinear Wave Equation on {R}^{3+1} |
| Autore | Burzio Stefano |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2022 |
| Descrizione fisica | 1 online resource (88 pages) |
| Disciplina |
515/.353
515.353 |
| Altri autori (Persone) | KriegerJoachim |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Nonlinear wave equations
Blowing up (Algebraic geometry) Perturbation (Mathematics) Asymptotic expansions Iterative methods (Mathematics) Fourier transformations Partial differential equations -- Hyperbolic equations and systems -- Wave equation Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions |
| ISBN |
9781470471699
1470471698 |
| Classificazione | 35L0535B40 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Cover -- Title page -- Chapter 1. Introduction -- 1.1. The type II blow up solutions of [33], [32] -- 1.2. The effect of symmetries on the solutions of Theorem 1.1 -- 1.3. Conditional stability of type II solutions -- 1.4. Spectral theory associated with the linearisation ℒ -- 1.5. Description of the data perturbation in terms of the distorted Fourier transform -- 1.6. Outline of the main result from [26] -- 1.7. Figures -- Chapter 2. The main theorem and outline of the proof -- 2.1. The main theorem -- 2.2. Outline of the proof -- Chapter 3. Construction of a two parameter family of approximate blow up solutions -- 3.1. Step 0: the bulk term -- 3.2. Step 1: choice of the first correction ₁ -- 3.3. Step 2: the ₁ error -- 3.4. Step 3: choice of second correction ₂ -- 3.5. Step 4: the ₂ error -- 3.6. Step 5: inductive step -- 3.7. Step 6: choice of _{ ℎ, }, =1,2 -- Chapter 4. Modulation theory -- determination of the parameters _{1,2}. -- 4.1. Re-scalings and the distorted Fourier transform -- 4.2. The effect of scaling the bulk part -- Chapter 5. Iterative construction of blow up solution almost matching the perturbed initial data -- 5.1. Formulation of the perturbation problem on Fourier side -- 5.2. The proof of Theorem 5.1 -- 5.3. Translation to original coordinate system -- Chapter 6. Proof of Theorem 2.1 -- Chapter 7. Outlook -- Bibliography -- Index -- Back Cover. |
| Record Nr. | UNINA-9911132800403321 |
| Burzio Stefano | ||
| Providence : , : American Mathematical Society, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||