Titlebook: Microlocal Analysis and Nonlinear Waves; Michael Beals,Richard B. Melrose,Jeffrey Rauch Conference proceedings 1991 Springer-Verlag New Yo

搖曳的微光

incredulity

裂隙

Regularity of Nonlinear Waves Associated with a Cusp,nsmooth at the singularity of the cusp. If . is a Tricomi operator associated with the cusp, and the natural initial data (Dirichlet or Cauchy) are conormal with respect to a hyperplane, then . is again shown to be conormal with respect to the cusp.

FLACK

THROB

兇殘

wreathe

Nonlinear Resonance Can Create Dense Oscillations,ing the mechanism which can produce such a phenomenon. The next two sections complete the construction of such solutions. The last section discusses some special considerations for the case of quadratic nonlinearities. We would like to acknowledge the help of our friends, Jean Fresnel with §2 and Jon Hunter with §4.

Ceramic

Conormality, Cusps and Non-Linear Interaction,ounded elements in these spaces form algebras and that they have appropriate solvability properties for certain linear differential operators. This leads to the general approach discussed here, mixing microlocalization and blow-up techniques.

GLUE

Quasimodes for the Laplace Operator and Glancing Hypersurfaces,the quasimode consists of the conic hull of the union of the bicharacteristics of the cosphere bundle .*Ω issuing from a family of invariant tori of the billiard ball map. To construct a quasimode near a gliding ray we find a global symplectic normal form for a pair of glancing hypersurfaces.

MOT

Infinite Gain of Regularity for Dispersive Evolution Equations, of Kato appears to depend on special a priori estimates, some of its mystery has been resolved by the recent results of finite regularity for various other nonlinear dispersive equations due to Constantin and Saut [1], Ponce [5] and others [3]. However, all of them require growth conditions on the nonlinear term.