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1.
Summary
In this paper we prove the existence of periodic solutions of abstract evolution equations which are modelled after parabolic problems. More precisely we prove that existence results follow from degree type hypotheses on the «projection» of the problem onto a suitable finite dimensional space. 相似文献
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Jianping Wu 《Applied mathematics and computation》2010,217(4):1764-1770
In this paper, using the extended tanh-function method, new explicit traveling wave solutions including rational solutions for three nonlinear evolution equations are obtained with the aid of Mathematica. 相似文献
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Ísmail Aslan 《Mathematical Methods in the Applied Sciences》2012,35(6):716-722
Problems that are modeled by nonlinear evolution equations occur in many areas of applied sciences. In the present study, we deal with the negative order KdV equation and the generalized Zakharov system and derive some further results using the so‐called first integral method. By means of the established first integrals, some exact traveling wave solutions are obtained in a concise manner. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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?smail Aslan 《Applied mathematics and computation》2011,217(20):8134-8139
In this paper, we show the applicability of the first integral method, which is based on the ring theory of commutative algebra, to the regularized long-wave Burgers equation and the Gilson-Pickering equation under a parameter condition. Our method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are derived in a concise manner. 相似文献
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In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate the algorithm. At the same time, some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations, such as Camassa-Holm equation, Kolmogorov-Petrovskii-Piskunov equation, and so on. Then a direct constructive method called multi-auxiliary equations expansion method is described to derive the multi-solitary wave solutions of nonlinear evolution equations. Finally, a class of novel multi-solitary wave solutions of the (2+1)-dimensional asymmetric version of the Nizhnik-Novikov-Veselov equation are given by three direct methods. The algorithm proposed in this paper can be steadily applied to some other nonlinear problems. 相似文献
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Ramesh B. Kudenatti Vishwanath B. AwatiN.M. Bujurke 《Applied mathematics and computation》2011,218(6):2952-2959
Third order nonlinear ordinary differential equations, subject to appropriate boundary conditions arising in fluid dynamics, are solved using three different methods viz., the Dirichlet series, method of stretching of variables, and asymptotic function method. Similarity transformations are used to convert the governing partial differential equations into nonlinear ordinary differential equations. The numerical results obtained from the above methods for various problems are given in terms of skin friction. Our study revealed that the results obtained from these methods agree well with those of direct numerical simulation of ordinary differential equations. Also, these methods have advantages over pure numerical methods in obtaining derived quantities such as velocity profile accurately for various values of the parameters at a stretch. 相似文献
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Caisheng Chen Hui Wang ShengLan Zhu 《Mathematical Methods in the Applied Sciences》2011,34(5):497-508
In this work, we prove the existence of global attractor for the nonlinear evolution equation utt?Δu?Δut?Δutt + g(x, u)=f(x) in X=(H2(Ω)∩H(Ω)) × (H2(Ω)∩H(Ω)). This improves a previous result of Xie and Zhong in (J. Math. Anal. Appl. 2007; 336 :54–69.) concerning the existence of global attractor in H(Ω) × H(Ω) for a similar equation. Further, the asymptotic behavior and the decay property of global solution are discussed. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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研究了一类非线性演化方程初值问题.通过不变子空间方法,这类初值问题被约化为常微分方程组的初值问题.这类初值问题是适定的.本文给出了这类初值问题关于时间变量t的幂级数解. 相似文献
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It is shown in this paper that three types of matrix equations AX−XF=BY,AX−EXF=BY and which have wide applications in control systems theory, are equivalent to the matrix equation with their coefficient matrices satisfying some relations. Based on right coprime factorization to , explicit solutions to the equation are proposed and thus explicit solutions to the former three types of matrix equations can be immediately established. With the special structure of the proposed solutions, necessary conditions to the nonsingularity of matrix X are also obtained. The proposed solutions give an ultimate and unified formula for the explicit solutions to these four types of linear matrix equations. 相似文献
12.
Anti-periodic solutions to nonlinear evolution equations 总被引:1,自引:0,他引:1
Liu Zhenhai 《Journal of Functional Analysis》2010,258(6):2026-5009
We deal with anti-periodic problems for nonlinear evolution equations with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. 相似文献
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Michele Bartuccelli Guido Gentile James A. Wright 《Applied Mathematics Letters》2013,26(10):1026-1030
We present a class of Hill’s equations possessing explicit solutions through elementary functions. In addition we provide some applications by using some of the paradigmatic systems of classical dynamics, such as the pendulum with variable length. 相似文献
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Yongqin Xie Chengkui Zhong 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5095-5105
In this paper, using a new method (or technology), we prove the existence and upper semi-continuity of the global attractors Aω for a class of nonlinear evolution equations in D(A)×D(A), where the nonlinear term f satisfies a critical exponential growth condition. 相似文献
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利用双函数法和吴消元法,得到了一类非线性演化方程在不同情况下的一系列显示精确解.Sinh-Gordon方程及Klein-Gordon方程作为该方程的特例也得到了相应的行波解. 相似文献
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We study in this paper the initial value problem for the multivalued differential equation wheref is in MS(2) andG is a multifunction fromC([0, T];) into the closed subsets of L2(0, Y;), satisfying suitable regularity assumptions. As an application we prove a local existence result for the problem
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F.J. Massey 《Journal of Differential Equations》1976,22(2):416-427
Analyticity in t of solutions u(t) of nonlinear evolution equations of the form , is established under suitable conditions on . An application is given to quasilinear parabolic equations. 相似文献
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The infinite-delay-differential equations (IDDEs) are studied and the analytic solution of a class of nonlinear IDDEs is presented based on the characteristics of the reproducing kernel space W2[0,∞). Besides, the exact solution is represented in the form of series. It is proved that the n-term approximation un(x) converges to the exact solution u(x) of the IDDEs. Moreover, the approximate error of un(x) is monotone decreasing. The results of experiments showed that the proposed method in this paper is computationally efficient. 相似文献
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