Caustics for Dissipative Semilinear Oscillations.
Joly, Jean-Luc.
Caustics for Dissipative Semilinear Oscillations. - 1st ed. - 1 online resource (87 pages) - Memoirs of the American Mathematical Society ; v.144 . - Memoirs of the American Mathematical Society .
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.
9781470402761
Differential equations, Hyperbolic -- Numerical solutions.
Differential equations, Nonlinear -- Numerical solutions.
Electronic books.
QA377 -- .J65 2000eb
510 s;515/.353
Caustics for Dissipative Semilinear Oscillations. - 1st ed. - 1 online resource (87 pages) - Memoirs of the American Mathematical Society ; v.144 . - Memoirs of the American Mathematical Society .
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.
9781470402761
Differential equations, Hyperbolic -- Numerical solutions.
Differential equations, Nonlinear -- Numerical solutions.
Electronic books.
QA377 -- .J65 2000eb
510 s;515/.353