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41.
On the properties of solutions to the Goursat-Darboux problem with boundary and distributed controls
N. I. Pogodaev 《Siberian Mathematical Journal》2007,48(5):897-912
We consider a control system described by the Goursat-Darboux equation. The system is controlled by distributed and boundary controls. The controls are subject to the constraints given as multivalued mappings with closed, possibly nonconvex, values depending on the phase variable. Alongside the initial constraints, we consider the convexified constraints and the constraints whose values are the extreme points of the convexified constraints. We study the questions of existence of solutions and establish connections between the solutions under various constraints. 相似文献
42.
Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries 总被引:2,自引:0,他引:2
Ling-hua KONG~ 《中国科学A辑(英文版)》2007,50(9):1251-1266
This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented. 相似文献
43.
Wing-Sum Cheung Patricia J.Y. Wong 《Journal of Mathematical Analysis and Applications》2007,329(2):851-869
We consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments. Using Schauder fixed point theorem, we establish criteria such that the system of boundary value problems has at least one fixed-sign solution. 相似文献
44.
T. Roubíček 《Journal of Optimization Theory and Applications》2007,132(1):41-50
Existence of a Nash equilibrium in a noncooperative game governed by the one-dimensional Burgers equation, proposed in the
case of pointwise controls in Ref. 1, is proved under data qualifications that guarantee the diffusion term in the Burgers’
equation to be dominant enough with respect to the uniform convexity of the payoffs.
This work was partly supported by Grants 201/03/0934 (GA čR) and MSM 0021620839 (MšMT čR). Inspiring discussions with Angel
M. Ramos are acknowledged. 相似文献
45.
Alexandre N. Carvalho German Lozada-Cruz 《Journal of Mathematical Analysis and Applications》2007,325(2):1216-1239
We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of eigenvalues and eigenfunctions of the Laplace operator in such domains. This information is used to show that the asymptotic dynamics of the heat equation in this domain is equivalent to the asymptotic dynamics of a system of two ordinary differential equations diffusively (weakly) coupled. The main tools employed are the invariant manifold theory and a uniform trace theorem. 相似文献
46.
工况图在热电厂的设计和运行中具有广泛的用途。本文根据引进型双抽非再热200MW供热机组的技术特点,通过编程在纯凝汽工况、单抽工业抽汽工况、单抽采暖抽汽工况和双抽供热等典型变工况计算的基础上,完成了当新蒸汽负荷、工业抽汽负荷和采暖抽汽负荷发生改变时的变工况计算,并绘制了该机组的运行工况图. 相似文献
47.
In this paper we formulate a theorem on the persistence of elliptic lower-dimensional invariant tori for nearly integrable analytic Hamiltonian systems under the first Melnikov condition and Rüssmann’s non-degeneracy condition, and give the measure estimates of parameters for the non-resonance conditions under Rüssmann’s non-degeneracy condition, which is essential for the proof of our result. 相似文献
48.
We consider the 3D Navier–Stokes equation with generalized impermeability boundary conditions. As auxiliary results, we prove the local in time existence of a strong solution (‘strong’ in a limited sense) and a theorem on structure. Then, taking advantage of the boundary conditions, we formulate sufficient conditions for regularity up to the boundary of a weak solution by means of requirements on one of the eigenvalues of the rate of deformation tensor. Finally, we apply these general results to the case of an axially symmetric flow with zero angular velocity. 相似文献
49.
W. Kotarski 《Journal of Optimization Theory and Applications》1987,54(3):565-573
Combining the results of Walczak (Ref. 1) and Lasiecka (Refs. 2 and 3), we extend the well-known Dubovicki-Milutin theorem in two directions: (i) We allow for treatment of several equality constraints in optimization problems; and (ii) We assume less regularity of optimization problems by requiring the existence of external cones instead of tangent cones. An example of an optimization problem is also considered. 相似文献
50.
B. V. Pal’tsev I. I. Chechel’ 《Computational Mathematics and Mathematical Physics》2006,46(5):820-847
The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 103. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ~ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ~ 5 × 103. 相似文献