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Caustics for Dissipative Semilinear Oscillations.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2000Copyright date: ©2000Edition: 1st edDescription: 1 online resource (87 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470402761
Subject(s): Genre/Form: Additional physical formats: Print version:: Caustics for Dissipative Semilinear OscillationsDDC classification:
  • 510 s;515/.353
LOC classification:
  • QA377 -- .J65 2000eb
Online resources:
Contents:
Intro -- Contents -- 1. Introduction -- 2. Notations and main results -- 2.1. The time evolution -- 2.2. Lagrangians, caustics and phases -- 2.3. L[Sup(p)] estimates of oscillatory integrals -- 2.4. Oscillations and profiles -- 2.5. Sketch of the main results -- 2.6. Remarks and examples -- 3. L[Sup(p)] estimates for oscillatory integrals -- 3.1. Statement of the main estimate -- 3.2. Proof of Theorem 3.1.1 -- 3.3. Proof of Theorem 3.1.2 -- 3.4. Proof of Theorem 3.1.3 -- 3.5. Subcritical L[Sup(p)] estimates for Iε(A) -- 4. Oscillations and profiles -- 4.1. Estimates for Jε(A) and Iε(A) -- 4.2. Extension to nonsmooth profiles -- 4.3. Weak profiles -- 5. The nonlinear interaction operators -- 5.1. The interaction operators for profiles -- 5.2. Profiles of nonlinear functions of oscillations -- 6. Proof of asymptotics -- 6.1. Weak convergence -- 6.2. Construction of approximate solutions -- 6.3. Strong convergences -- 6.4. Uniqueness for the profile equations -- 6.5. The main result -- 6.6. Absorption at supercritical points -- 6.7. Angular smoothness for profiles -- 7. Additional results and remarks -- 7.1. The wave equation -- 7.2. Lipschitzean nonlinearities and nonstrictly monotone nonlinearities -- 7.3. Nonlinear interaction and transfer of singularities above the caustic -- 8. References.
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Intro -- Contents -- 1. Introduction -- 2. Notations and main results -- 2.1. The time evolution -- 2.2. Lagrangians, caustics and phases -- 2.3. L[Sup(p)] estimates of oscillatory integrals -- 2.4. Oscillations and profiles -- 2.5. Sketch of the main results -- 2.6. Remarks and examples -- 3. L[Sup(p)] estimates for oscillatory integrals -- 3.1. Statement of the main estimate -- 3.2. Proof of Theorem 3.1.1 -- 3.3. Proof of Theorem 3.1.2 -- 3.4. Proof of Theorem 3.1.3 -- 3.5. Subcritical L[Sup(p)] estimates for Iε(A) -- 4. Oscillations and profiles -- 4.1. Estimates for Jε(A) and Iε(A) -- 4.2. Extension to nonsmooth profiles -- 4.3. Weak profiles -- 5. The nonlinear interaction operators -- 5.1. The interaction operators for profiles -- 5.2. Profiles of nonlinear functions of oscillations -- 6. Proof of asymptotics -- 6.1. Weak convergence -- 6.2. Construction of approximate solutions -- 6.3. Strong convergences -- 6.4. Uniqueness for the profile equations -- 6.5. The main result -- 6.6. Absorption at supercritical points -- 6.7. Angular smoothness for profiles -- 7. Additional results and remarks -- 7.1. The wave equation -- 7.2. Lipschitzean nonlinearities and nonstrictly monotone nonlinearities -- 7.3. Nonlinear interaction and transfer of singularities above the caustic -- 8. References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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