摘要:

The multi‐duality of the nonlinear variational problem infJ(u, Λu) is studied for minimal surfaces‐type problems. By using the method developed by Gao and Strang [1], the Fenchel‐Rockafellar's duality theory is generalized to the problems with affine operator Λ. Two dual variational principles are established for nonparametric surfaces with constant mean curvature. We show that for the same primal problem, there may exist different dual problems. The primal problem may or may not possess a solution, whereas each dual problem possesses a unique solution. An evolutionary method for solving the nonlinear optimal‐shape design problem is presented with numerica

ISSN:0022-2526    

DOI:10.1002/sapm1995952127

年代:1995

数据来源: WILEY

摘要:

This paper studies the asymptotic solution of the initial‐boundary value problem for scalar convection‐dominated evolution equations on a bounded spatial domain when initial and boundary conditions are such that the solution develops a single thin shock layer of steep change. The exponentially slow motion of the shock is determined for exponentially long times using an ansatz based on the solution for the special case of Burgers' equation, obtained through the Cole‐Hopf transformation. Results obtained analytically are confirmed by numerical experi

ISSN:0022-2526    

DOI:10.1002/sapm1995952147

年代:1995

数据来源: WILEY

ISSN:0022-2526    

DOI:10.1002/sapm1995952171

年代:1995

数据来源: WILEY

摘要:

A constructive analytical procedure is described for generating a class of solutions pertaining to the fluid velocity field satisfying the three‐dimensional Navier‐Stokes equations. The arbitrary functions occurring in the solution are related to those that arise in the general solution of the Stokes and Oseen equati

ISSN:0022-2526    

DOI:10.1002/sapm1995952193

年代:1995

数据来源: WILEY

摘要:

The nim‐like game 〈n, f; X, Y〉 is defined by an integern≥ 2 a constraint functionf, and two players andXandY. PlayersXandYalternate taking coins from a pile ofncoins, withXtaking the first turn. The winner is the one who takes the last coin. On thekth turn, a player may removetkcoins, where 1 ≤t1≤n− 1 and 1 ≤tk≤ max{1,f(tk−1) fork>1. Let the setSf= {1} ∪ {n| there is a winning strategy forYin the nim‐like game 〈n,f;X,Y〉}. In this paper, an algorithm is provided to construct the setSf= {a1,a2,…} in an increasing sequence when the functionf(x) is monotonic. We show that if the functionf(x) is linear, then there exist integersn0andmsuch thatan+1=an+an−mforn>n0and we give upper and lower bounds form(dependent onf. A duality is established between the asymptotic order of the sequence of elements inSfand the degree of the functionf(x). A necessary and sufficient condition for the sequence {a0,a1,a2,…} of elements inSfto satisfy a regular recurre

ISSN:0022-2526    

DOI:10.1002/sapm1995952213

年代:1995

数据来源: WILEY