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We wish to construct an optimal optical lens, in the sense that it focuses all rays from a given source onto a given focal point. The construction can be reduced mathematically to a global study of a system of two nonlinear functional differential equations. We prove that this system has precisely two analytic solutions. 相似文献
34.
In this paper we study linear reaction–hyperbolic systems of the form , (i = 1, 2, ..., n) for x > 0, t > 0 coupled to a diffusion equation for p
0 = p
0(x, y, θ, t) with “near-equilibrium” initial and boundary data. This problem arises in a model of transport of neurofilaments in axons.
The matrix (k
ij
) is assumed to have a unique null vector with positive components summed to 1 and the v
j
are arbitrary velocities such that . We prove that as the solution converges to a traveling wave with velocity v and a spreading front, and that the convergence rate in the uniform norm is , for any small positive α. 相似文献
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J. Marshall Ash Jonathan Cohen Gang Wang 《Journal of Fourier Analysis and Applications》1995,2(5):507-517
The Cauchy problem and global well-posedness for a mathematical model of the strong interaction of two-dimensional, long,
internal gravity waves propogating on neighboring pycnoclines in a stratified fluid have been studied by Bona, Ponce, Saut,
Tom, and others. We show that global well-posedness occurs even when the initial data is rough. 相似文献
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Sunto Un problema di frontiera libera (moto di un fluido attraverso una diga in terra non omogenea) è ricondotto allo studio di
una disequazione variazionale. Si danno condizioni sul coefficiente di permeabilità sufficienti ad assicurare che la parte
bagnata della diga è un sottografico.
Entrata in Redazione il 30 giugno 1976.
This paper is partially supported by National Science Foundation Grant MPS 72-04959 A02, and by C.N.R. of Italy through L.A.N. of Pavia. 相似文献
Entrata in Redazione il 30 giugno 1976.
This paper is partially supported by National Science Foundation Grant MPS 72-04959 A02, and by C.N.R. of Italy through L.A.N. of Pavia. 相似文献