Geometric Optics Expansions for Hyperbolic Corner Problems II: From Weak Stability to Violent Instability
نویسندگان
چکیده
منابع مشابه
Geometric Optics Expansions for Hyperbolic Corner Problems II: From Weak Stability to Violent Instability
In this article we are interested in the rigorous construction of geometric optics expansions for weakly well-posed 4 hyperbolic corner problems. More precisely we focus on the case where selfinteracting phases occur and where one of them is 5 exactly the phase where the uniform Kreiss-Lopatinskii condition fails. We show that the associated WKB expansion suffers 6 arbitrarily many amplificatio...
متن کاملGeometric Optics Expansions with Amplification for Hyperbolic Boundary Value Problems: Linear Problems
We compute and justify rigorous geometric optics expansions for linear hyperbolic boundary value problems that do not satisfy the uniform Lopatinskii condition. We exhibit an amplification phenomenon for the reflection of small high frequency oscillations at the boundary. Our analysis has two important consequences for such hyperbolic boundary value problems. Firstly, we make precise the optima...
متن کاملHyperbolic Partial Differential Equations and Geometric Optics
§1.1. The method of characteristics §1.2. Examples of propagation of singularities using progressing waves §1.3. Group velocity and the method of nonstationary phase §1.4. Fourier synthesis and rectilinear propagation §1.5. A cautionary example in geometric optics §1.6. The law of reflection §1.6.1. The method of images §1.6.2. The plane wave derivation §1.6.3. Reflected high frequency wave pac...
متن کاملComplex Geometric Optics for Symmetric Hyperbolic Systems Ii: Nonlinear Theory in One Space Dimension
This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always satisfy the naive coherence condition on the complex phases, which is required in the construction of the approximate solution. Formally the theory applies also...
متن کاملGeometric Optics and Instability for Semi-classical Schrödinger Equations
We prove some instability phenomena for semi-classical (linear or) nonlinear Schrödinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2017
ISSN: 0036-1410,1095-7154
DOI: 10.1137/16m1060145