2,538 research outputs found
Boundary clustered layer positive solutions for an elliptic Neumann problem with large exponent
Let be a smooth bounded domain in with ,
we study the existence and profile of positive solutions for the following
elliptic Neumann problem where is a large exponent and
denotes the outer unit normal vector to the boundary . For
suitable domains , by a constructive way we prove that, for any
integers , with and , if is large enough,
such a problem has a family of positive solutions with interior layers and
boundary layers which concentrate along distinct -dimensional
minimal submanifolds of , or collapse to the same
-dimensional minimal submanifold of as
A wave near the edge of a circular disk
It is shown that in the Love-Kirchhoff plate theory, an edge wave can travel
in a circular thin disk made of an isotropic elastic material. This disk edge
wave turns out to be faster than the classic flexural acoustic wave in a
straight-edged, semi-infinite, thin plate, a wave which it mimics when the
curvature radius becomes very large compared to the wavelength
Crossflow effects on the growth rate of inviscid Goertler vortices in a hypersonic boundary layer
The effects of crossflow on the growth rate of inviscid Goertler vortices in a hypersonic boundary layer with pressure gradient are studied. Attention is focused on the inviscid mode trapped in the temperature adjustment layer; this mode has greater growth rate than any other mode. The eigenvalue problem which governs the relationship between the growth rate, the crossflow amplitude, and the wavenumber is solved numerically, and the results are then used to clarify the effects of crossflow on the growth rate of inviscid Goertler vortices. It is shown that crossflow effects on Goertler vortices are fundamentally different for incompressible and hypersonic flows. The neutral mode eigenvalue problem is found to have an exact solution, and as a by-product, we have also found the exact solution to a neutral mode eigenvalue problem which was formulated, but unsolved before, by Bassom and Hall (1991)
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