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61.
A. B. Vasil’eva A. A. Plotnikov 《Computational Mathematics and Mathematical Physics》2006,46(5):762-767
A singularly perturbed parabolic equation with a nonlinear right-hand side of a special form is examined. A numerical analytical study of such equations is performed. 相似文献
62.
C. P. Massarolo G. P. Menzala A. F. Pazoto 《Mathematical Methods in the Applied Sciences》2007,30(12):1419-1435
The aim of this work is to consider the Korteweg–de Vries equation in a finite interval with a very weak localized dissipation namely the H?1‐norm. Our main result says that the total energy decays locally uniform at an exponential rate. Our analysis improves earlier works on the subject (Q. Appl. Math. 2002; LX (1):111–129; ESAIM Control Optim. Calculus Variations 2005; 11 (3):473–486) and gives a satisfactory answer to a problem suggested in (Q. Appl. Math. 2002; LX (1):111–129). Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
63.
64.
Differential inequality method, bounding function method and topological degree are applied to obtain the existence criterions of at least one solution for the general fourth-order differential equations under nonlinear boundary conditions, and many existing results are complemented. 相似文献
65.
Effect of Weakly Transverse Perturbations on Dust Acoustic Solitary Waves with Adiabatic Variation of Dust Charge 总被引:1,自引:0,他引:1
DUAN Wen-Shan 《理论物理通讯》2002,38(12)
By employing the reductive perturbation technique we derived a Kadomtsev-Petviashvili equation forunmagnetized dusty plasmas. It suggests that the nonlinear dust acoustic solitary waves with adiabatic variation of dustcharge are stable even there are some higher order transverse perturbatoins. There are only rarefactive solitary wavesfor this system which has been verified analytically in this paper. 相似文献
66.
YAN Zhen-Ya 《理论物理通讯》2002,38(10)
Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations. 相似文献
67.
Barotropic FRW cosmologies are presented from the standpoint of nonrelativistic supersymmetry. First, we reduce the barotropic FRW system of differential equations to simple harmonic oscillator differential equations. Employing the factorization procedure, the solutions of the latter equations are divided into the two classes of bosonic (nonsingular) and fermionic (singular) cosmological solutions. We next introduce a coupling parameter denoted by K between the two classes of solutions and obtain barotropic cosmologies with dissipative features acting on the scale factors and spatial curvature of the universe. The K-extended FRW equations in comoving time are presented in explicit form in the low coupling regime. The standard barotropic FRW cosmologies correspond to the dissipationless limit K = 0. 相似文献
68.
Ling-yan Tang Song-he Song 《应用数学学报(英文版)》2007,23(2):303-310
In this paper,we use Daubechies scaling functions as test functions for the Galerkin method,and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations.It can be proved that the schemesare TVD schemes.Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations.Furthermore,they have high-order accuracy in smooth regions and good resolution of singularities. 相似文献
69.
A functional equation of nonlinear iterates is discussed on the circle S1 for its continuous solutions and differentiable solutions. By lifting to R, the existence, uniqueness and stability of those solutions are obtained. Techniques of continuation are used to guarantee the preservation of continuity and differentiability in lifting. 相似文献
70.
Antoni Leon Dawidowicz Najemedin Haribash Anna Poskrobko 《Mathematical Methods in the Applied Sciences》2007,30(7):779-787
The problem of the existence of the invariant measure is important considering its connections with chaotic behaviour. In the papers (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123; Ann. Pol. Math. 1983; XLI :129–137; J. Differential Equations 2004; 196 :448–465) the existence of invariant and ergodic measures according to the dynamical system generated by the Lasota equation was proved, i.e. the equation describing the dynamics and becoming different of the population of cells. In this paper, the existence of such measure for the quasi‐linear Lasota equation is proved. This measure is the carriage of the measure described by Dawidowicz (Zesz. Nauk. Uniw. Jagiellońskiego, Pr. Mat. 1982; 23 :117–123). Copyright © 2006 John Wiley & Sons, Ltd. 相似文献