首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到19条相似文献,搜索用时 156 毫秒
1.
This paper concerns a system of nonlinear wave equations describing the vibrations of a 3-dimensional network of elastic strings.The authors derive the equations and appropriate nodal conditions,determine equilibrium solutions,and,by using the methods of quasilinear hyperbolic systems,prove that for tree networks the natural initial,boundary value problem has classical solutions existing in neighborhoods of the "stretched" equilibrium solutions.Then the local controllability of such networks near such equilibrium configurations in a certain specified time interval is proved.Finally,it is proved that,given two different equilibrium states satisfying certain conditions,it is possible to control the network from states in a small enough neighborhood of one equilibrium to any state in a suitable neighborhood of the second equilibrium over a suffciently large time interval.  相似文献   

2.
In this paper, the authors consider a system of degenerate Davey-Stewartson equations. They prove the global existence of weak solutions in some weighted function spaces and the decay of weak solutions in some anisotropic spaces for appropriate initial data.  相似文献   

3.
李兴校  曹林芬 《数学季刊》2007,22(3):344-351
The paper studies a class of nonlinear elliptic partial differential equations on a compact Riemannian manifold (M,g) with some curvature restriction.The authors try to prove some uniqueness and nonexistent results for the positive solutions of the equations concerned.  相似文献   

4.
The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.  相似文献   

5.
In this paper, the authors study the existence of periodic solutions to an evolution p-Laplacian system. The authors prove a comparison principle of the system in general form. Then the existence of periodic solutions to the system of evolution p-Laplacian equations is obtained with the help of the comparison principle and the monotone iteration technique.  相似文献   

6.
The exact boundary controllability and the exact boundary observability for the 1-D first order linear hyperbolic system were studied by the constructive method in the framework of weak solutions in the work [Lu, X. and Li, T. T., Exact boundary controllability of weak solutions for a kind of first order hyperbolic system — the constructive method, Chin. Ann. Math. Ser. B, 42(5), 2021, 643–676]. In this paper, in order to study these problems from the viewpoint of duality, the authors establish ...  相似文献   

7.
In this paper,the convergence of time-dependent Euler-Maxwell equations to compressible Euler-Poisson equations in a torus via the non-relativistic limit is studied. The local existence of smooth solutions to both systems is proved by using energy esti- mates for first order symmetrizable hyperbolic systems.For well prepared initial data the convergence of solutions is rigorously justified by an analysis of asymptotic expansions up to any order.The authors perform also an initial layer analysis for general initial data and prove the convergence of asymptotic expansions up to first order.  相似文献   

8.
The authors study a resonant Klein-Gordon system with convenient nonlinearities in two space dimensions, prove that such a system has global solutions for small, smooth, compactly supported Cauchy data, and find that the asymptotic profile of the solution is quite different from that of the free solution.  相似文献   

9.
The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains.  相似文献   

10.
This paper is concerned with backward stochastic differential equations with Poisson jumps under some weak assumptions. We prove the existence and uniqueness of the adapted solution, which extends the result of Situ (Stoch. Process. Appl., (1997) 66) to the case where the monotonicity conditions (Briand, Stoch. Process. Appl., (2003) 108) is satisfied, using the extended Bihari inequality and a series of approximate equations. The stability of the solutions can also be obtained for such kind of equations.  相似文献   

11.
This paper concerns a non-linear system of wave equations describing the motion in space of an elastic string. We derive the equations, determine the equilibrium solutions and, using the methods of quasilinear hyperbolic systems, prove that the natural initial, boundary value problem has classical solutions existing in neighbourhoods of the “stretched” equilibrium solutions. We then prove that the positions of the endpoints of the string can be controlled in such a way that the string moves from an equilibrium in one location to an equilibrium in another location.  相似文献   

12.
A simplified n-dimensional BAM neural network model with delays is considered. Some results of Hopf bifurcations occurring at the zero equilibrium as the delay increases are exhibited. Global existence of periodic solutions are established using a global Hopf bifurcation result of Wu [Wu J. Symmetric functional-differential equations and neural networks with memory. Trans Am Math Soc 1998;350:4799–838], and a Bendixson criterion for higher dimensional ordinary differential equations due to Li and Muldowney [Li MY, Muldowney J. On Bendixson’s criterion. J Differ Equations 1994;106:27–39]. Finally, computer simulations are performed to illustrate the analytical results found.  相似文献   

13.
In this paper we provide a characterization of second order fully nonlinear CR invariant equations on the Heisenberg group, which is the analogue in the CR setting of the result proved in the Euclidean setting by A. Li and the first author in Li and Li (2003) [21]. We also prove a comparison principle for solutions of second order fully nonlinear CR invariant equations defined on bounded domains of the Heisenberg group and a comparison principle for solutions of a family of second order fully nonlinear equations on a punctured ball.  相似文献   

14.
The dynamics of a Nicholson's blowflies equation with a finite delay are investigated. We prove that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived, using the theory of normal form and center manifold. Global existence of periodic solutions are established using a global Hopf bifurcation result of Wu (Trans. Amer. Math. Soc. 350 (1998) 4799), and a Bendixson criterion for higher dimensional ordinary differential equations due to Li and Muldowney (J. Differential Equations 106 (1994) 27).  相似文献   

15.
Singularly perturbed nonautonomous ordinary differential equations are studied for which the associated equations have equilibrium states consisting of at least two intersecting curves, which leads to exchange of stabilities of these equilibria. The asymptotic method of differential equations is used to derive conditions under which initial value problems have solutions characterized by immediate and delayed exchange of stabilities. These results are then used to prove the existence of periodic canard solutions. Published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 1, pp. 46–61. The text was submitted by the authors in English.  相似文献   

16.
This paper deals with asymptotic behavior of solutions to a heat system with absorptions and coupling positive multi-nonlinearities. It is known that although absorption mechanisms may affect such as blow-up criteria, blow-up time, and initial data required for blow-up solutions, they cannot change blow-up rates of solutions in general. It has been reported in the current literature that blow-up rates for scalar equations with absorptions are all absorption-independent. In a previous paper of the authors, four absorption-independent simultaneous blow-up rates were obtained already for the same problem under weak absorptions. The present paper will furthermore prove that if the absorptions are unbalanced in the model (i.e., the absorption is stronger for one component and weaker for another), then there are in addition eight possible absorption-related blow-up rates for the model, besides the four absorption-independent ones. This exposes a significant difference between scalar and coupled nonlinear parabolic equations with absorptions.  相似文献   

17.
本文主要在多维空间中讨论一类发展型p-Laplace方程及方程组的初边值问题.这类问题在非牛顿渗流方程的理论研究中有着重要的意义.作者通过上、下解的方法证明了发展型p-Laplace方程解的整体有限性;同时利用两个关于常微分方程的比较原理,给出了相应的方程组解的整体有限性结果.  相似文献   

18.
The dynamics of a food-limited population model with delay are investigated. We prove that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived, using the theory of normal form and center manifold. Global existence of periodic solutions is established by using a global Hopf bifurcation result due to [J. Wu, Symmetric functional differential equations and neural networks with memory, Trans. Amer. Math. Soc. 350 (1998) 4799–4838].  相似文献   

19.
We study quasilinear elliptic equations with strong nonlinear terms and systems of such equations. The methods developed by the authors in [1], [2] are used to prove the existence of solutions for boundary—value problems using some information on behavior of potential bounds for nonlinearities; the L–characteristics of elliptic operators and their fractional powers play an important role. New conditions are suggested for the existence of classical solutions of quasilinear second order elliptic equations.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号