共查询到20条相似文献,搜索用时 31 毫秒
1.
M. R. Gonzalez-Dorrego 《Mathematische Nachrichten》1994,165(1):133-158
In this paper the asymptotic behaviour of the solutions of x' = A(t)x + h(t,x) under the assumptions of instability is studied, A(t) and h(t,x) being a square matrix and a vector function, respectively. The conditions for the existence of bounded solutions or solutions tending to the origin as t → ∞ are obtained. The method: the system is recasted to an equation with complex conjugate coordinates and this equation is studied by means of a suitable Lyapunov function and by virtue of the Wazevski topological method. Applications to a nonlinear differential equation of the second order are given. 相似文献
2.
Claire Chainais‐Hillairet 《Mathematical Methods in the Applied Sciences》2000,23(5):467-490
We study second‐order finite‐volume schemes for the non‐linear hyperbolic equation ut(x, t) + div F(x, t, u(x, t)) = 0 with initial condition u0. The main result is the error estimate between the approximate solution given by the scheme and the entropy solution. It is based on some stability properties verified by the scheme and on a discrete entropy inequality. If u0 ∈ L∞ ∩ BVloc(ℝN), we get an error estimate of order h1/4, where h defines the size of the mesh. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
3.
In this paper, we give some sufficient conditions to guarantee global asymptotic stability of the zero solution of the third‐order nonlinear differential equation: x ′ ′ ′ + g(x,x ′ ,x ′ ′ ) + f(x,x ′ )x ′ + h(x) = 0. Two examples are also given to illustrate our results. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
4.
In this article, an iterative method for the approximate solution to one‐dimensional variable‐coefficient Burgers' equation is proposed in the reproducing kernel space W(3,2). It is proved that the approximation wn(x,t) converges to the exact solution u(x,t) for any initial function w0(x,t) ε W(3,2), and the approximate solution is the best approximation under a complete normal orthogonal system . Moreover the derivatives of wn(x,t) are also uniformly convergent to the derivatives of u(x,t).© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
5.
Hong Gu 《Mathematical Methods in the Applied Sciences》2016,39(3):344-352
We consider the Fisher–KPP equation with advection: ut=uxx?βux+f(u) on the half‐line x∈(0,∞), with no‐flux boundary condition ux?βu = 0 at x = 0. We study the influence of the advection coefficient ?β on the long time behavior of the solutions. We show that for any compactly supported, nonnegative initial data, (i) when β∈(0,c0), the solution converges locally uniformly to a strictly increasing positive stationary solution, (ii) when β∈[c0,∞), the solution converges locally uniformly to 0, here c0 is the minimal speed of the traveling waves of the classical Fisher–KPP equation. Moreover, (i) when β > 0, the asymptotic positions of the level sets on the right side of the solution are (β + c0)t + o(t), and (ii) when β≥c0, the asymptotic positions of the level sets on the left side are (β ? c0)t + o(t). Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
6.
Let h : ? → ? be a computable function. A real number x is called h‐monotonically computable (h‐mc, for short) if there is a computable sequence (xs) of rational numbers which converges to x h‐monotonically in the sense that h(n)|x – xn| ≥ |x – xm| for all n andm > n. In this paper we investigate classes h‐ MC of h‐mc real numbers for different computable functions h. Especially, for computable functions h : ? → (0, 1)?, we show that the class h‐ MC coincides with the classes of computable and semi‐computable real numbers if and only if Σi∈?(1 – h(i)) = ∞and the sum Σi∈?(1 – h(i)) is a computable real number, respectively. On the other hand, if h(n) ≥ 1 and h converges to 1, then h‐ MC = SC (the class of semi‐computable reals) no matter how fast h converges to 1. Furthermore, for any constant c > 1, if h is increasing and converges to c, then h‐ MC = c‐ MC . Finally, if h is monotone and unbounded, then h‐ MC contains all ω‐mc real numbers which are g‐mc for some computable function g. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
《Mathematical Methods in the Applied Sciences》2018,41(9):3294-3306
In this article, we consider the asymptotic behavior of the classical solution to the 3‐dimensional Vlasov‐Poisson plasma interacting repulsively with N point charges. The large time behavior in terms of diameters of its velocity‐spatial supports is improved to O(t2/3+ϵ) for any ϵ>0. 相似文献
8.
This paper studies the existence and the non‐existence of global solutions to the initial boundary value problems for the non‐linear wave equation utt + uxxxx = σ(ux)x + f(x, t) and the Boussinesq‐type equation utt + uxxxx = σ(u)xx + f(x, t). The paper proves that every above‐mentioned problem has a unique global solution under rather mild confining conditions, and arrives at some sufficient conditions of blow‐up of the solutions in finite time. Finally, a few examples are given. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
9.
Two classes of asymptotically different positive solutions to advanced differential equations via two different fixed‐point principles
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The paper considers a system of advanced‐type functional differential equations where F is a given functional, , r > 0 and xt(θ) = x(t + θ), θ∈[0,r]. Two different results on the existence of solutions, with coordinates bounded above and below by the coordinates of the given vector functions if t→∞, are proved using two different fixed‐point principles. It is illustrated by examples that, applying both results simultaneously to the same equation yields two positive solutions asymptotically different for t→∞. The equation where a,τ∈(0,∞), a < 1/(τe), are constants can serve as a linear example. The existence of a pair of positive solutions asymptotically different for t→∞ is proved and their asymptotic behavior is investigated. The results are also illustrated by a nonlinear equation. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
10.
R. K. Mohanty Dinesh Kumar M. K. Jain 《Numerical Methods for Partial Differential Equations》2003,19(3):327-342
In this article, using a single computational cell, we report some stable two‐level explicit finite difference approximations of O(kh2 + h4) for ?u/?n for three‐space dimensional quasi‐linear parabolic equation, where h > 0 and k > 0 are mesh sizes in space and time directions, respectively. When grid lines are parallel to x‐, y‐, and z‐coordinate axes, then ?u/?n at an internal grid point becomes ?u/?x, ?u/?y, and ?u/?z, respectively. The proposed methods are also applicable to the polar coordinates problems. The proposed methods have the simplicity in nature and use the same marching type of technique of solution. Stability analysis of a linear difference equation and computational efficiency of the methods are discussed. The results of numerical experiments are compared with exact solutions. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 327–342, 2003. 相似文献
11.
《Mathematical Methods in the Applied Sciences》2018,41(4):1578-1599
We consider the linearized thermoelastic plate equation with the Dirichlet boundary condition in a general domain Ω, given by with the initial condition u|(t=0)=u0, ut|(t=0)=u1, and θ|(t=0)=θ0 in Ω and the boundary condition u=∂νu=θ=0 on Γ, where u=u(x,t) denotes a vertical displacement at time t at the point x=(x1,⋯,xn)∈Ω, while θ=θ(x,t) describes the temperature. This work extends the result obtained by Naito and Shibata that studied the problem in the half‐space case. We prove the existence of ‐bounded solution operators of the corresponding resolvent problem. Then, the generation of C0 analytic semigroup and the maximal Lp‐Lq‐regularity of time‐dependent problem are derived. 相似文献
12.
It is well‐known that every planar graph has a vertex of degree at most five. Kotzig proved that every 3‐connected planar graph has an edge xy such that deg(x) + deg (y) ≤ 13. In this article, considering a similar problem for the case of three or more vertices that induce a connected subgraph, we show that, for a given positive integer t, every 3‐connected planar graph G with |V(G)| ≥ t has a connected subgraph H of order t such that Σx∈V(H) degG(x) ≤ 8t − 1. As a tool for proving this result, we consider decompositions of 3‐connected planar graphs into connected subgraphs of order at least t and at most 2t − 1. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 191–203, 1999 相似文献
13.
We consider the asymptotic nonlinear filtering problem dx=f(x)dt + ?1/2 dw,dy=h(x) dt + ? dv and obtain lim?→0 ? log q 2(x,t) = -W(x,t) for unnormalized conditional densities q 2(x,t) using PDE methods. HereW(x,t) is the value function for a deterministic optimal control problem arising in Mortensen's deterministic estimation, and is the unique viscosity solution of a Hamilton-Jacobi-Bellman equation. ijab has also studied this filtering problem, and we extend his large deviation result for certain unnormalized conditional measures. The resulting variational problem corresponds to the above control problem 相似文献
14.
This paper deals with the solutions defined for all time of the KPP equation ut = uxx + f(u), 0 < u(x,t) < 1, (x,t) ∈ ℝ2, where ƒ is a KPP‐type nonlinearity defined in [0,1]: ƒ(0) = ƒ(1) = 0, ƒ′(0) > 0, ƒ′(1) < 0, ƒ > 0 in (0,1), and ƒ′(s) ≤ ƒ′(0) in [0,1]. This equation admits infinitely many traveling‐wave‐type solutions, increasing or decreasing in x. It also admits solutions that depend only on t. In this paper, we build four other manifolds of solutions: One is 5‐dimensional, one is 4‐dimensional, and two are 3‐dimensional. Some of these new solutions are obtained by considering two traveling waves that come from both sides of the real axis and mix. Furthermore, the traveling‐wave solutions are on the boundary of these four manifolds. © 1999 John Wiley & Sons, Inc. 相似文献
15.
Nonoscillation criteria for second‐order nonlinear differential equations with decaying coefficients
Jitsuro Sugie 《Mathematische Nachrichten》2008,281(11):1624-1637
This paper is concerned with the problem of deciding conditions on the coefficient q (t) and the nonlinear term g (x) which ensure that all nontrivial solutions of the equation (|x ′|α–1x ′)′ + q (t)g (x) = 0, α > 0, are nonoscillatory. The nonlinear term g (x) is not imposed no assumption except for the continuity and the sign condition xg (x) > 0 if x ≠ 0. In our problem, it is important to examine the relation between the decay of q (t) and the growth of g (x). Our main result extends some nonoscillation theorem for the generalised Emden–Fowler equation. Proof is given by means of some Liapunov functions and phase‐plane analysis. A simple example is includes to show that the monotonicity of g (x) is not essential in our problem. Finally, elliptic equations with the m ‐Laplacian operator are discussed as an application to our results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
M. H. Lantsman 《Mathematische Nachrichten》1997,186(1):197-223
In this paper the asymptotic properties as t → + ∞ for a single linear differential equation of the form x(n) + a1 (t)x(n?1)+…. + an(t)x = 0, where the coefficients aj (z) are supposed to be of the power order of growth, are considered. The results obtained in the previous publications of the author were related to the so called regular case when a complete set of roots {λ,(t)}, j = 1, 2, …, n of the characteristic polynomial yn + a1 (t)yn?1 + … + an(t) possesses the property of asymptotic separability. One of the main restrictions of the regular case consists of the demand that the roots of the set {λ,(t)} have not to be equivalent in pairs for t → + ∞. In this paper we consider the some more general case when the set of characteristic roots possesses the property of asymptotic independence which includes the case when the roots may be equivdent in pairs. But some restrictions on the asymptotic behaviour of their differences λi(t)→ λj(t) are preserved. This case demands more complicated technique of investigation. For this purpose the so called asymptotic spaces were introduced. The theory of asymptotic spaces is used for formal solution of an operator equation of the form x = A(x) and has the analogous meaning as the classical theory of solving this equation in Band spaces. For the considered differential equation, the main asymptotic terms of a fundamental system of solution is given in a simple explicit form and the asymptotic fundamental system is represented in the form of asymptotic Emits for several iterate sequences. 相似文献
17.
The paper presents existence results for positive solutions of the differential equations x ″ + μh (x) = 0 and x ″ + μf (t, x) = 0 satisfying the Dirichlet boundary conditions. Here μ is a positive parameter and h and f are singular functions of non‐positone type. Examples are given to illustrate the main results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
In this paper, we employ a well‐known fixed point theorem for cones to study the existence of positive periodic solutions to the n ‐dimensional system x ″ + A (t)x = H (t)G (x). Moreover, the eigenvalue intervals for x ″ + A (t)x = λH (t)G (x) are easily characterized. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
Under what conditions is it true that if there is a graph homomorphism G □ H → G □ T, then there is a graph homomorphism H→ T? Let G be a connected graph of odd girth 2k + 1. We say that G is (2k + 1)‐angulated if every two vertices of G are joined by a path each of whose edges lies on some (2k + 1)‐cycle. We call G strongly (2k + 1)‐angulated if every two vertices are connected by a sequence of (2k + 1)‐cycles with consecutive cycles sharing at least one edge. We prove that if G is strongly (2k + 1)‐angulated, H is any graph, S, T are graphs with odd girth at least 2k + 1, and ?: G□ H→S□T is a graph homomorphism, then either ? maps G□{h} to S□{th} for all h∈V(H) where th∈V(T) depends on h; or ? maps G□{h} to {sh}□ T for all h∈V(H) where sh∈V(S) depends on h. This theorem allows us to prove several sufficient conditions for a cancelation law of a graph homomorphism between two box products with a common factor. We conclude the article with some open questions. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:221‐238, 2008 相似文献
20.
Antonio Campo 《Numerical Methods for Partial Differential Equations》2004,20(6):820-830
The principal goal of this article is to present two asymptotic solutions for the classical Graetz‐Nusselt problem. The method of lines (MOL) has been adopted for solving the governing partial differential energy equation in two independent variables in an asymptotic manner. Two temperature subfields are determined semianalytically: one for small x (x → 0) and the other for large x (x → ∞). Later, the two asymptotic mean Nusselt number subdistributions, Nu X→0(x) and Nu X→∞(x), blend themselves into a generalized correlation equation for the mean Nusselt number distribution Nu (x) covering the entire x‐domain. The simplicity of the MOL procedure, combined with the high quality asymptotic mean Nusselt number subdistributions, provides an alternative methodology for solving the Graetz‐Nusselt problem without using higher level mathematics. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. 相似文献