Transition layer for the heterogeneous Allen–Cahn equation

Transition Layer for the Heterogeneous Allen-Cahn Equation

We consider the equation (1) ε∆u = (u− a(x))(u − 1) in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω is a smooth and bounded domain in R, ν the outer unit normal to ∂Ω, and a a smooth function satisfying −1 < a(x) < 1 in Ω. We set K, Ω+ and Ω− to be respectively the zero-level set of a, {a > 0} and {a < 0}. Assuming ∇a 6= 0 on K and a 6= 0 on ∂Ω, we show that there exists a sequence εj → 0 such that equation (1)...

Layer Stripping for the Helmholtz Equation

A Mediation Layer for Heterogeneous XML Schemas

This paper describes an approach for mediation of heterogeneous XML schemas. Such an approach is proposed as a tool for XML data integration system. A global XML schema is specified by the designer to provide a homogeneous view over heterogeneous XML data. An XML mediation layer is introduced to manage: (1) establishing appropriate mappings between the global schema and the schemas of the sourc...

Asymptotic receptivity analysis and the Parabolized Stability Equation : a combined approach to boundary layer transition

We consider the interaction of free-stream disturbances with the leading edge of a body and its effect on the transition point. We present a method which combines an asymptotic receptivity approach, and a numerical method which marches through the Orr-Sommerfeld region. The asymptotic receptivity analysis produces a three deck eigensolution which in its far downstream limiting form, produces an...

Boundary Layer for Chaffee-Infante Type Equation

This article is concerned with the nonlinear singular perturbation problem due to small diffusivity in nonlinear evolution equations of Chaffee-Infante type. The boundary layer appearing at the boundary of the domain is fully described by a corrector which is “explicitly” constructed. This corrector allows us to obtain convergence in Sobolev spaces up to the boundary. AMS Subject Classification...