摘要:

An asymptotic solution of the linear shallow water equations for small Rossby number is constructed to describe Ross by waves. It leads to a dispersion or eiconal equation for the phase of the waves and a transport equation for their amplitude. It is shown how these equations can be solved by means of rays for both planetary and topographic Rossby waves. The method is illustrated by constructing the wave field produced by a time harmonic point source in fluid of uniform depth. This solution is a Green's function for the equations.

ISSN:0022-2526    

DOI:10.1002/sapm1995944359

年代:1995

数据来源: WILEY

摘要:

This paper deals with a new proof of the existence of weak solutions to scalar conservation laws. Our approach relies on the use of a particular finite difference scheme for time discretization which introduces a viscous term. The approximate solutions can be computed explicitly by solving a set of linear ordinary differential problems. We prove that they converge towards a weak solution which is, in a certain sense, unique and stable.

ISSN:0022-2526    

DOI:10.1002/sapm1995944377

年代:1995

数据来源: WILEY

摘要:

A new multiple‐scale perturbation technique is employed to find the approximate solution to a fairly general matrix system of ordinary differential equations. This system includes a linear part given by a slowly‐varying matrix and a small nonlinear part. The general proof of the method given in previous work is used to show rigorously that the present approximate solution is indeed asymptotic to the solution of the differential system. Some typical special cases of the general solution are also gi

ISSN:0022-2526    

DOI:10.1002/sapm1995944393

年代:1995

数据来源: WILEY

摘要:

We prove a surprisingly high lower bound for the number of magic squares.

ISSN:0022-2526    

DOI:10.1002/sapm1995944415

年代:1995

数据来源: WILEY

摘要:

The nonlinear eigenvalue problem in buckling analysis is studied for von Kármán plates. By using the general duality theory developed by Gao‐Strang [1, 2] it is proved that the stability criterion for the bifurcated state depends on a reduced complementary gap function. The duality theory is established for nonlinear bifurcation problems. This theory shows that the nonlinear eigenvalue problem is eventually equivalent to a coupled quadratic dual optimization problem. A series of equivalent variational principles are constructed and a lower bound theorem for the first eigenvalue of the buckling factor is pro

ISSN:0022-2526    

DOI:10.1002/sapm1995944423

年代:1995

数据来源: WILEY