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1.
Some relatively simple techniques are applied to a singular control problem arising in bioeconomics. First, Stokes' theorem is applied to the fixed-endpoint problem. This reduces the free-endpoint problem to a problem in ordinary calculus. It is then possible to find an explicit expression for the switching manifold, which generalizes the results obtained by Cliff and Vincent (Ref. 1).  相似文献   

2.
One studies the initial-boundary value problem for the Stokes' system, arising at the investigation of the nonstationary motion of two viscous fluids, separated by a free surface. Junction conditions are prescribed in the plane ×3=0}. The consideration of the surface tension leads to a noncoercive integral term in the condition for the jump of the normal stresses. The unique solvability and estimates of the solution in Hölder classes of functions of the given model problem are proved with the aid of a theorem on Fourier multipliers and a significant part of the paper is devoted to the proof of the required modifications of this theorem.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 188, pp. 5–44, 1991.  相似文献   

3.
We present formulations of the Trotter-Kato theorem for approximation of linear C-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes' equation as illustrative examples.

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4.
In this paper an asymptotic stability result is estabilished for the compressible navier-Stokes equations. Since the Mach number tends to zero, the incompressible limit solution of compressible Navier-Stokes equations is proved to be stable exponentially. Some results of Stokes' problem are used.  相似文献   

5.
In this paper, integrals of second kind over a rectifiable curve or a piecewise smooth surface are extended to continuous fractal curves and surfaces. Theorems for the existence of these integrals are proved. Green's, Gauss' and Stokes' theorems are developed for domains with fractal boundaries.  相似文献   

6.
Summary We introduce two families of mixed finite element on conforming inH(div) and one conforming inH(curl). These finite elements can be used to approximate the Stokes' system.  相似文献   

7.
Summary In this paper we prove the existence of the integral of differential forms with cornpact support on stratified subsets of Rn with locally finite volume and toe give some sufficient conditions to have Stokes' formula on regular stratified sets.  相似文献   

8.
Following Longuet-Higgins' (1978) discovery of some new relationsbetween Stokes' coefficients in the theory of gravity waves,it is shown that similar relations may be derived for the coefficientsof the highest wave (on deep water) solution of Longuet-Higgins& Fox (1978). These new relations allow the solution tobe computed more easily.  相似文献   

9.
In a recent paper Longuet-Higgins (1978) discovered some newrelations between Stokes' coefficients in the theory of periodicgravity waves. These were shown to give rise to a set of integralrelations. In this paper we show that this set is complete inthe sense that it is equivalent to Bernoulli's equation. Wealso show that a suitably redefined set exists in the theoryof the solitary wave.  相似文献   

10.
Summary We study in this paper a new mixed finite element approximation of the Stokes' problem in the velocity pressure formulation. This approximation which is based on a new variational principle allows the use of low order Lagrange elements and leads to optimal order of convergence for the velocity and the pressure. Iterative and direct methods for the solution of the approximate problems will be discussed in a forthcoming paper.  相似文献   

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