共查询到20条相似文献,搜索用时 15 毫秒
1.
Given any wave speed c∈R, we construct a traveling wave solution of ut=Δu+2|∇u|u in an infinitely long cylinder, which connects two locally stable and axially symmetric steady states at x3=±∞. Here u is a director field with values in S2⊂R3: |u|=1. The traveling wave has a singular point on the cylinder axis. In view of the bistable character of the potential, the result is surprising, and it is intimately related to the nonuniqueness of the harmonic map flow itself. We show that for only one wave speed the traveling wave behaves locally, near its singular point, as a symmetric harmonic map. 相似文献
2.
Solitary wave solutions for a family of nonlinear evolution equations with an arbitrary parameter in the exponents are constructed. Some of the obtained solutions seem to be new. 相似文献
3.
Jonatan Lenells 《Journal of Mathematical Analysis and Applications》2005,306(1):72-82
We classify all weak traveling wave solutions of the Degasperis-Procesi equation. In addition to smooth and peaked solutions, the equation is shown to admit more exotic traveling waves such as cuspons, stumpons, and composite waves. 相似文献
4.
The traveling wave solutions connecting two equilibria for a delayed Logistic equation in a cylinder are obtained for any delay . We attain our goal by using the approach based on the combination of Schauder fixed point theory and the weak coupled upper–lower solutions method. Moreover, we prove that there is a constant that serves as the minimal wave speed of such traveling wave solutions. 相似文献
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We consider the simplest possible heat equation for director fields, ut=Δu+|∇u|2u (|u|=1), and construct axially symmetric traveling wave solutions defined in an infinitely long cylinder. The traveling waves have a point singularity of topological degree 0 or 1. 相似文献
7.
In this paper, the traveling wave problem for a two-species competition reaction–diffusion–chemotaxis Lotka–Volterra system is investigated. Upper and lower solutions method and fixed point theory are employed to show the existence of traveling wave solutions connecting the coexistence constant steady state with zero state for all large enough wave speed , and conversely, when is small, we prove there is no traveling wave solution. 相似文献
8.
Kai Zhou 《Journal of Mathematical Analysis and Applications》2010,372(2):598-610
This paper deals with the existence of traveling wave solutions in delayed nonlocal diffusion systems with mixed monotonicity. Based on two different mixed-quasimonotonicity reaction terms, we propose new definitions of upper and lower solutions. By using Schauder's fixed point theorem and a new cross-iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The general results obtained have been applied to type-K monotone and type-K competitive nonlocal diffusive Lotka-Volterra systems. 相似文献
9.
This paper deals with the existence of traveling wave solutions in delayed reaction-diffusion systems with mixed monotonicity. Based on two different mixed-quasi monotonicity reaction terms, we propose new conditions on the reaction terms and new definitions of upper and lower solutions. By using Schauder’s fixed point theorem and a new cross-iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions. The general results obtained have been applied to type-K monotone and type-K competitive diffusive Lotka-Volterra systems. 相似文献
10.
Huijun Fan 《中国科学A辑(英文版)》1999,42(2):113-132
It is proved that the heat equations of harmonic maps have self-similar solutions satisfying certain energy condition. 相似文献
11.
Using the method of dynamical systems to study the coupled KdV system, some exact explicit parametric representations of the solitary wave and periodic wave solutions are obtained in the given parameter regions. Chaotic behavior of traveling wave solutions is determined. 相似文献
12.
We establish traveling wave solutions for the combustion model of a shear flow in a cylinder. We study two cases: the infinite Lewis number and an arbitrary Lewis number. For the infinite Lewis number, we establish the existence of traveling wave fronts for both non‐minimal and minimal speeds. For an arbitrary Lewis number, we establish the uniform bounds and exponential decay rates. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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In this paper, by using bifurcation method, we successfully find the Fornberg-Whitham equation
ut−uxxt+ux=uuxxx−uux+3uxuxx, 相似文献
14.
A. Cellina A. Ferriero 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2003,20(6):467-919
Under general growth assumptions, that include some cases of linear growth, we prove existence of Lipschitzian solutions to the problem of minimizing ∫abL(x(s),x′(s)) ds with the boundary conditions x(a)=A, x(b)=B. 相似文献
15.
Discretization of the harmonic map flow into spheres often uses a penalization or projection strategy, where the first suffers from the proper choice of an additional parameter, and the latter from the lack of a discrete energy law, and restrictive mesh-constraints. We propose an implicit scheme that preserves the sphere constraint at every node, enjoys a discrete energy law, and unconditionally converges to weak solutions of the harmonic map heat flow.
16.
Wenzhang Huang 《Journal of Mathematical Analysis and Applications》2006,316(1):42-59
The existence of traveling wave solutions for a reaction-diffusion, which serves as models for microbial growth in a flow reactor and for mathematical epidemiology, was previously confirmed. However, the problem on the uniqueness of traveling wave solutions remains open. In this paper we give a complete proof of the uniqueness of traveling wave solutions. 相似文献
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Nonlinear wave phenomena are of great importance in the nature, and have became for a long time a challenging research topic for both pure and applied mathematicians. In this paper the solitary wave, kink (anti-kink) wave and periodic wave solutions for a class of (3+1)-dimensional nonlinear equation were obtained by some effective methods from the dynamical systems theory. 相似文献
19.
In this paper, a measure-theoretical approach to find the approximate solutions for a class of first order nonlinear difference equations is introduced. In this method the problem is transformed to an equivalent optimization problem. Then, by considering it as a calculus of variations problem, some concepts in measure theory are used to approximate the solution. The procedure of constructing approximate solution in form of an algorithm is shown. Finally a numerical example is given. 相似文献
20.
In this paper we study traveling wave solutions of a non-cooperative lattice-diffusion system with time delay, which includes predator–prey models and disease-transmission models. Minimal wave speed of traveling wave solutions is given. Schauder’s fixed-point theorem is applied to show the existence of semi-traveling wave solutions. The boundness and persistence of traveling wave solutions are overcome by using rescaling method and Laplace transform, where the application of Laplace transform to persistence is very novel and creative. The traveling wave solutions for some specific models are shown to connect to a positive equilibrium by using Lyapunov function and LaSalle’s invariance principle. 相似文献