共查询到20条相似文献,搜索用时 46 毫秒
1.
考查了周期边界条件下的磁流体方程,证明了它的解关于时间是解析的,由此得到了磁流体方程的解的向后惟一性.对于周期解,证明了当周期小于某个常数时,周期的弱解是强解,进一步地这样的强解是定常解. 相似文献
2.
In this paper, we study a very simple three term recurrence relation involving the discontinuous Heaviside step function. One reason for studying such an relation is that solutions of our recurrence relation are steady state distributions in some basic neural network models. Since analytic tools cannot be used to handle discontinuous models such as ours, existence of periodic solutions is investigated by combining combinatorial elimination technique as well as existence arguments for linear systems. By such means, we are able to obtain all periodic solutions with least periods 1 through 9. Some periodic solutions with periods 15, 18, 42 and 72 can also be found, but exhaustive results are not yet available. 相似文献
3.
In this paper, we study a very simple three term recurrence relation involving the discontinuous Heaviside step function. One reason for studying such an relation is that solutions of our recurrence relation are steady state distributions in some basic neural network models. Since analytic tools cannot be used to handle discontinuous models such as ours, existence of periodic solutions is investigated by combining combinatorial elimination technique as well as existence arguments for linear systems. By such means, we are able to obtain all periodic solutions with least periods 1 through 8. Some periodic solutions with periods 12, 20 and 36 can also be found, but exhaustive results are not yet available. 相似文献
4.
A concept of a fundamental solution is introduced for linear operator equations given in some functional spaces. In the case where this fundamental solution does not exist, the representation of the solution is found by the concept of a generalized fundamental solution, which is introduced for operators with nontrivial and generally infinite-dimensional kernels. The fundamental and generalized fundamental solutions are also investigated for a class of Fredholm-type operator equations. Some applications are given for one-dimensional generally nonlocal hyperbolic problems with trivial, finite- and infinite-dimensional kernels. The fundamental and generalized fundamental solutions of such problems are constructed as particular solutions of a system of integral equations or an integral equation. These fundamental solutions become meaningful in a general case when the coefficients are generally nonsmooth functions satisfying only some conditions such as p-integrablity and boundedness. 相似文献
5.
Steve Tefteller 《Annali di Matematica Pura ed Applicata》1973,96(1):185-192
Summary This work is concerned with the behavior of solutions of third order self-adjoint differential equations. It is well known
that products of solutions of a second order self-adjoint equation are solutions of the third order equation. A converse of
this fact is established. Existence of oscillatory solutions and asymptotic behavior of nonoscillatory solutions is established.
Separation and comparison theorems are obtained for such equations.
Entrata in Redazione il 13 aprile 1972. 相似文献
6.
James M. Hill 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1989,40(6):872-882
Summary There is presently considerable interest in the utilization of microwave heating to novel industrial applications. Mathematically such problems involve Maxwell's equations coupled with the heat equation and for which all thermal, electrical and magnetic properties of the material are nonlinearly dependent upon temperature. Accordingly such problems are highly complex and very little theoretical work has been undertaken. The purpose of this paper is to obtain simple exact solutions applicable to microwave heating in the simplest situation, involving only one spatial dimension and assuming that all thermal, electrical and magnetic properties exhibit a power law dependence on temperature. Similarity solutions and other special solutions are examined. These generally result in highly nonlinear coupled systems of ordinary differential equations and although some new closed results are obtained in special cases, in general, such complex systems of ordinary differential equations need to be solved numerically. Roughly speaking, we show that stretching similarity solutions exist only if the power law electrical and thermal conductivities and magnetic permeability with indicesl, m andn respectively are such thatl+m+n=0. Similar constraints on the indices apply for the existence of other simple solutions. 相似文献
7.
Gen-Qiang Wang 《Journal of Difference Equations and Applications》2013,19(2):261-304
Doubly periodic travelling waves can be used to describe dynamic patterns of signals that govern movements of animals. In this paper, we study the existence of such waves in cellular networks involving the discontinuous Heaviside step function. This is done by finding ω-periodic solutions of an accompanying recurrence relation with a priori unknown parameters and the Heaviside function. Since analytic tools cannot be used to handle discontinuous models such as ours, existence of periodic solutions is investigated by means of symmetry, combinatorial techniques and accompanying linear systems. By such means, we are able to obtain all periodic solutions with least periods 1 through 6. Our techniques are new and good for other periodic solutions with relatively small periods. 相似文献
8.
Roman Cherniha Maksym Didovych 《Communications in Nonlinear Science & Numerical Simulation》2013,18(11):2960-2971
Lie symmetries of a simplified Keller–Segel system are found and applied for construction of exact solutions. The algorithms for constructing all possible traveling wave and self-similar solutions of the system in question are presented. Several families of such solutions in an explicit form are found, their properties examined and possible applicability for chemotaxis modeling is discussed. 相似文献
9.
一类广义四阶非线性Camassa-Holm方程的行波解 总被引:1,自引:1,他引:0
用动力系统的分支理论研究了一类广义四阶非线性Camassa-Holm方程的动力学行为和行波解,发现方程存在一些孤立波解,周期波解和一些诸如Compacton类型的非光滑行波解.在不同的参数条件下,给出了这些解存在的条件和一些特殊条件下的精确解. 相似文献
10.
首先给出了运输问题最优解的相关概念,将最优解扩展到广义范畴,提出狭义多重最优解和广义多重最优解的概念及其区别.然后给出了惟一最优解、多重最优解、广义有限多重最优解、广义无限多重最优解的判定定理及其证明过程.最后推导出了狭义有限多重最优解个数下限和广义有限多重最优解个数上限的计算公式,并举例验证了结论的正确性. 相似文献
11.
Wenrui Hao Jonathan D. Hauenstein Bei Hu Andrew J. Sommese 《Applied mathematics and computation》2011,218(6):2661-2669
The growth of tumors can be modeled as a free boundary problem involving partial differential equations. We consider one such model and compute steady-state solutions for this model. These solutions include radially symmetric solutions where the free boundary is a sphere and nonradially symmetric solutions. Linear and nonlinear stability for these solutions are determined numerically. 相似文献
12.
Gui–Qiang Chen 《偏微分方程通讯》2013,38(8-9):1461-1487
Hyperbolic systems of conservaiton laws with a symmetry are studied. Some peculiar phenomena for such systems are shown. Admissibility criteria for solutions to such systems are discussed. propagation and cancellation of initial oscillations for the systems are classified. As a byproduct of this study, an existence theorem of global solutions for the Cauchy of the systems is established. 相似文献
13.
A. A. Amosov A. E. Vestfalsky 《Computational Mathematics and Mathematical Physics》2006,46(4):691-718
The Bakhvalov-Eglit two-scale homogenized equations are used to describe the motion of layered periodic compressible media with rapidly oscillating data. A new finite-difference scheme for a system of such equations is proposed and analyzed in the case of a thermoviscoelastic Voigt-type body. A priori estimates of solutions are derived for nonsmooth data. The existence and uniqueness of discrete solutions are established. A theorem is proved on the convergence of a subsequence of discrete solutions to a weak solution of the problem under study. Simultaneously, a new theorem on the existence of global weak solutions is deduced. 相似文献
14.
Weiqin Yu Na Li Fangqi Chen Shouwei Zhao 《Journal of Applied Analysis & Computation》2016,6(4):968-980
Utilizing the methods of dynamical system theory, the Dullin-Gottwald-Holm equation is studied in this paper. The dynamical behaviors of the traveling wave solutions and their bifurcations are presented in different parameter regions. Furthermore, the exact explicit forms of all possible bounded solutions, such as solitary wave solutions, periodic wave solutions and breaking loop wave solutions are obtained. 相似文献
15.
Analytical blowup solutions to the 2-dimensional isothermal Euler-Poisson equations of gaseous stars
Manwai Yuen 《Journal of Mathematical Analysis and Applications》2008,341(1):445-456
We study the Euler-Poisson equations of describing the evolution of the gaseous star in astrophysics. Firstly, we construct a family of analytical blowup solutions for the isothermal case in R2. Furthermore the blowup rate of the above solutions is also studied and some remarks about the applicability of such solutions to the Navier-Stokes-Poisson equations and the drift-diffusion model in semiconductors are included. Finally, for the isothermal case (γ=1), the result of Makino and Perthame for the tame solutions is extended to show that the life span of such solutions must be finite if the initial data is with compact support. 相似文献
16.
Gary M. Lieberman 《Annali dell'Universita di Ferrara》2011,57(1):121-172
We study a class of second elliptic equations whose highest order coefficients vanish everywhere on the boundary. Under suitable
conditions on the lower order coefficients, Langlais proved in 1985 that such equations have unique smooth solutions up to
the boundary provided the data are smooth enough. Our goal here is to prove some Schauder estimates for these equations and
to obtain results even in Lipschitz domains. In addition, we show that bounded solutions of such problems are as smooth as
the data allow. A key step is to observe that smooth solutions must satisfy an oblique derivative boundary condition. 相似文献
17.
N. T. Levashova N. N. Nefedov A. V. Yagremtsev 《Computational Mathematics and Mathematical Physics》2013,53(3):273-283
For a singularly perturbed parabolic equation termed in applications as the reaction-diffusion-advection equation, stationary solutions with internal transition layers (contrast structures) are studied. An arbitrary-order asymptotic approximation of such solutions is constructed, and an existence theorem is proved. An efficient algorithm for constructing an asymptotic approximation of the transition point is proposed. The constructed asymptotic approximation is justified by applying the asymptotic method of differential inequalities, which is extended to the class of problems under study. This method is also used to establish the Lyapunov stability of such stationary solutions. 相似文献
18.
It is shown that in many cases globally defined, bounded solutions of evolution equations are as smooth (in time) as the corresponding operator, even if a general solution of the initial-value problem is much less smooth; i.e., initial values for bounded solutions are selected in such a way that optimal smoothness is attained. In particular, solutions which bifurcate from certain steady states, such as periodic orbits, almost-periodic orbits and also homo- and heteroclinic orbits, have this property. As examples, a neutral functional differential equation, a slightly damped non-linear wave equation, and a heat equation are considered. In the latter case the space variable is included into the discussion of smoothness. Finally, generalized Hopf bifurcation in infinite dimensions is considered. Here smoothness of the bifurcation function is discussed and known results on the order of a focus are generalized. 相似文献
19.
20.
Arie Leizarowitz 《Applied Mathematics and Optimization》1986,14(1):155-171
A tracking problem on an infinite time interval is studied, where the plant is linear with quadratic cost, and the tracked trajectory is not necessarily period. Optimal solutions with respect to the overtaking criterion are studied. Existence and uniqueness of such optimal solutions are proved and they are shown to be given by a linear feedback law which is the same as in the periodic case. A close relation between the solutions of tracking problems where the tracked trajectories are different only for very large times is established. 相似文献