共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we generalize the main theorem of Liz and Ferreiro [E. Liz, J.B. Ferreiro, A note on the global stability of generalized difference equations, Appl. Math. Lett. 15 (2002) 655–659] and some other global stability results for nonautonomous higher-order difference equations to the case when contraction-type steps are incorporated together with the steps when the difference sequence can increase. 相似文献
2.
Mei Jianqin Huang Dingjiang Zhang Hongqing 《Communications in Nonlinear Science & Numerical Simulation》2009,14(11):3798-3803
Using the idea of transformation, some links between (2 + 1)-dimensional nonlinear evolution equations and the ordinary differential equations Painlevé-II equations has been illustrated. The Kadomtsev–Petviashvili (KP) equation, generalized (2 + 1)-dimensional break soliton equation and (2 + 1)-dimensional Boussinesq equation are researched. As a result, some new interesting results about these (2 + 1)-dimensional PDEs have been obtained, such as the exact solutions with arbitrary functions, rich rational solutions and the nontrivial Bäcklund transformations have been derived. 相似文献
3.
This paper deals with the existence of mild L-quasi-solutions to the initial value problem for a class of semilinear impulsive evolution equations in an ordered Banach space E. Under a new concept of upper and lower solutions, a new monotone iterative technique on the initial value problem of impulsive evolution equations has been established. The results improve and extend some relevant results in ordinary differential equations and partial differential equations. An example is also given. 相似文献
4.
求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt算法 总被引:10,自引:0,他引:10
本文提出了求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt算法,即μk=ακ(θ||F_k|| (1-θ)||J_k~TF_k||),θ∈[0,1],其中ακ利用信赖域技巧来修正.在不必假设雅可比矩阵非奇异的局部误差界条件下,证明了该算法是全局收敛和局部二次收敛的.数值试验表明该算法能有效地求解奇异非线性方程组问题. 相似文献
5.
By using the continuation theorem due to Mawhin and Gaines, some analysis techniques and the Lyapunov functional method, the sufficient conditions ensuring the existence of an exponential periodic attractor of a class of impulsive differential equations with time-varying delays are established. The results are interesting and very different from previously known results [Xia and Wong, 2009 [7]; Tan and Tan, 2009 [19]; Huang et al., 2005 [20]; Liu and Huang, 2006 [22]]. Finally, applications and an example are given to illustrate the effectiveness of the results. 相似文献
6.
In this paper, the effect electric field on the flow induced by the combined buoyancy and thermocapillary forces is carried out. Calculations are performed for a strong unipolar injection (C = 10) and different values of Marangoni number (−10000 ≤ Ma ≤ 10000), thermal Rayleigh number (5000 ≤ Ra ≤ 50,000) and electric Rayleigh number (0 ≤ T ≤ 800). The Prandtl number (Pr) and the mobility parameter (M) are fixed at 116.6 and 49, respectively. These values correspond to the Silicone oil used as working liquid several practical applications. The full set of coupled equations: Navier–Stokes, Electro-hydrodynamic (EHD) and heat transfer equations are directly solved using stream function-vorticity formalism. Obtained results show that the electric forces can control the thermocapillary instabilities. According to the intensity and the direction of the applied electric forces, it is demonstrated that these instabilities can be accentuated, attenuated, or even completely eliminated. 相似文献
7.
Cyclic reduction is an algorithm invented by G. H. Golub and R. W. Hockney in the mid 1960s for solving linear systems related
to the finite differences discretization of the Poisson equation over a rectangle. Among the algorithms of Gene Golub, it
is one of the most versatile and powerful ever created. Recently, it has been applied to solve different problems from different
applicative areas. In this paper we survey the main features of cyclic reduction, relate it to properties of analytic functions,
recall its extension to solving more general finite and infinite linear systems, and different kinds of nonlinear matrix equations,
including algebraic Riccati equations, with applications to Markov chains, queueing models and transport theory. Some new
results concerning the convergence properties of cyclic reduction and its applicability are proved under very weak assumptions.
New formulae for overcoming breakdown are provided. 相似文献
8.
In this paper, we are concerned with the partial regularity for suitable weak solutions of the tri-dimensional magnetohydrodynamic equations. With the help of the De Giorgi iteration method, we obtain the results proved by He and Xin (C. He, Z. Xin, Partial regularity of suitable weak solutions to the incompressible magnetohydrodynamic equations, J. Funct. Anal. 227 (2005) 113–152), namely, the one dimensional parabolic Hausdorff measure of the possible singular points of the velocity field and the magnetic field is zero. 相似文献
9.
M.L. Gandarias M. RedondoM.S. Bruzón 《Nonlinear Analysis: Real World Applications》2012,13(1):340-347
In Gandarias (2011) [12] one of the present authors has introduced the concept of weak self-adjoint equations. This definition generalizes the concept of self-adjoint and quasi self-adjoint equations that were introduced by Ibragimov (2006) [11]. In this paper we find a class of weak self-adjoint Hamilton-Jacobi-Bellman equations which are neither self-adjoint nor quasi self-adjoint. By using a general theorem on conservation laws proved in Ibragimov (2007) [9] and the new concept of weak self-adjointness (Gandarias, 2011) [12] we find conservation laws for some of these partial differential equations. 相似文献
10.
In this paper, we study a class of nonlinear operator equations x = Ax + x
0 on ordered Banach spaces, where A is a monotone generalized concave operator. Using the properties of cones and monotone iterative technique, we establish
the existence and uniqueness of solutions for such equations. In particular, we do not demand the existence of upper-lower
solutions and compactness and continuity conditions. As applications, we study first-order initial value problems and two-point
boundary value problems with the nonlinear term is required to be monotone in its second argument. In the end, applications
to nonlinear systems of equations and to nonlinear matrix equations are also considered. 相似文献
11.
We consider higher order parabolic equations in divergence form with measurable coefficients to find optimal regularity in
Orlicz spaces of the maximum order derivatives of the weak solutions. The relevant minimal regularity requirement on the tensor
matrix coefficients is of small BMO in the spatial variable and is measurable in the time variable. As a consequence we prove
the classical W
m,p
regularity, m = 1, 2, . . . , 1 < p < ∞, for such higher order equations. In the same spirit the results easily extend to higher order parabolic systems as well
as up to the boundary. 相似文献
12.
Salih Yalinba Mehmet Sezer Hüseyin Hilmi Sorkun 《Applied mathematics and computation》2009,210(2):334-349
In this study, a Legendre collocation matrix method is presented to solve high-order Linear Fredholm integro-differential equations under the mixed conditions in terms of Legendre polynomials. The proposed method converts the equation and conditions to matrix equations, by means of collocation points on the interval [−1, 1], which corresponding to systems of linear algebraic equations with Legendre coefficients. Thus, by solving the matrix equation, Legendre coefficients and polynomial approach are obtained. Also examples that illustrate the pertinent features of the method are presented and by using the error analysis, the results are discussed. 相似文献
13.
Jan W. Cholewa Anibal Rodriguez-Bernal 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(8):3510-3530
It is known that the concept of dissipativeness is fundamental for understanding the asymptotic behavior of solutions to evolutionary problems. In this paper we investigate the dissipative mechanism for some semilinear fourth-order parabolic equations in the spaces of Bessel potentials and discuss some weak conditions that lead to the existence of a compact global attractor. While for second-order reaction–diffusion equations the dissipativeness mechanism has already been satisfactorily understood (see Arrieta et al. (2004), doi:10.1142/S0218202504003234 [7]), for higher order problems in unbounded domains it has not yet been fully developed. As shown throughout the paper, one of the main differences from the case of reaction–diffusion equations stems from the lack of a maximum principle. Thus we have to rely here on suitable energy estimates for the solutions. As in the case of second-order reaction–diffusion equations, we show here that both linear and nonlinear terms have to collaborate in order to produce dissipativeness. Thus, the dissipative mechanisms in second-order and fourth-order equations are similar, although the lack of a maximum principle makes the proofs more difficult and the results not as complete.Finally, we make essential use of the sharp results of Cholewa and Rodriguez-Bernal (2012), doi:10.1016/j.na.2011.08.022 [12], on linear fourth-order equations with a very large class of linear potentials. 相似文献
14.
For the numerical solution of stochastic differential equations an economical Runge–Kutta scheme of second order in the weak
sense is proposed. Numerical stability is studied and some examples are presented to support the theoretical results.
AMS subject classification (2000) 60H10 相似文献
15.
Jozef Džurina Said R. Grace Irena Jadlovská Tongxing Li 《Mathematische Nachrichten》2020,293(5):910-922
New oscillation criteria for the second-order Emden–Fowler delay differential equation with a sublinear neutral term are presented. An essential feature of our results is that oscillation of the studied equation is ensured via only one condition. Furthermore, as opposed to the results by Agarwal et al. (Ann. Mat. Pura Appl. (4) 193 (2014), no. 6, 1861–1875), Li and Rogovchenko (Math. Nachr. 288 (2015), no. 10, 1150–1162; Monatsh. Math. 184 (2017), no. 3, 489–500), and Xu (Monatsh. Math. 150 (2007), no. 2, 157–171), new criteria can be applied to Emden–Fowler delay differential equations with noncanonical operators and a sublinear neutral term. Our results essentially improve, extend, and simplify some known ones reported in the literature. The results are illustrated with examples. 相似文献
16.
The motion equations of a rigid body involve ten inertial characteristics: the mass, the mass center position and the inertia matrix. In order to identify these ten inertia characteristics, we propose an approach unifying them in a 4 × 4 positive definite symmetric matrix. The translation vector and the rotation matrix of the rigid body are also gathered in a 4 × 4 matrix. Therefore the motion equations are formulated as an equality between 4 × 4 skew–symmetric matrices: one representing the sum of external forces and torques, the second representing the dynamic force and torque. The identification is performed by a projected conjugate gradient algorithm developped in the 10–dimensional linear space of 4 × 4 symmetric matrices. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
Xiaoxiao Zheng Yadong Shang Xiaoming Peng 《Mathematical Methods in the Applied Sciences》2017,40(7):2623-2633
This paper investigates the orbital stability of solitary waves for the coupled Klein–Gordon–Zakharov (KGZ) equations where α ≠ 0. Firstly, we rewrite the coupled KGZ equations to obtain its Hamiltonian form. And then, we present a pair of sech‐type solutions of the coupled KGZ equations. Because the abstract orbital stability theory presented by Grillakis, Shatah, and Strauss (1987) cannot be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain the stability of the solitary waves for the coupled KGZ equations. In our work, α = 1,β = 0 are advisable. Hence, we can also obtain the orbital stability of solitary waves for the classical KGZ equations which was studied by Chen. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
18.
Existence of Generalized Traveling Waves in Time Recurrent and Space Periodic Monostable Equations 下载免费PDF全文
Wenxian Shen 《Journal of Applied Analysis & Computation》2011,1(1):69-94
This paper is concerned with the extension of the concepts and theories of traveling wave solutions of time and space periodic monostable equations to time recurrent and space periodic ones. It first introduces the concept of generalized traveling wave solutions of time recurrent and space periodic monostable equations, which extends the concept of periodic traveling wave solutions of time and space periodic monostable equations to time recurrent and space periodic ones. It then proves that in the direction of any unit vector \(\xi\), there is \(c^*(\xi)\) such that for any \(c>c^*(\xi)\), a generalized traveling wave solution in the direction of \(\xi\) with averaged propagation speed \(c\) exists. It also proves that if the time recurrent and space periodic monostable equation is indeed time periodic, then \(c^*(\xi)\) is the minimal wave speed in the direction of \(\xi\) and the generalized traveling wave solution in the direction of \(\xi\) with averaged speed \(c>c^*(\xi)\) is a periodic traveling wave solution with speed \(c\), which recovers the existing results on the existence of periodic traveling wave solutions in the direction of \(\xi\) with speed greater than the minimal speed in that direction. 相似文献
19.
S. Heikkilä 《Journal of Mathematical Analysis and Applications》2002,274(2):586-607
In this paper we apply the chain methods developed in (Heikkilä and Lakshmikantham, 1994) to obtain new fixed point theorems and new existence and comparison results for operator equations in partially ordered sets. These results are then applied to discontinuous implicit functional differential equations in ordered Banach spaces. 相似文献