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62.
In this paper, we first study the existence of transition fronts (generalized traveling fronts) for reaction-diffusion equations with the spatially heterogeneous bistable nonlinearity. By constructing sub-solution and super-solution we then show that transition fronts are globally exponentially stable for the solutions of the Cauchy problem. Furthermore, we prove that transition fronts are unique up to translation in time by using the monotonicity in time and the exponential decay of such transition fronts. 相似文献
63.
Guo-Bao Zhang 《Nonlinear Analysis: Real World Applications》2012,13(4):1790-1801
This paper is concerned with the global stability of traveling wave fronts of a non-local delayed lattice differential equation. By the comparison principle together with the semi-discrete Fourier transform, we prove that, all noncritical traveling wave fronts are globally stable in the form of t−1/αe−μt for some constants μ>0 and 0<α≤2, and the critical traveling wave fronts are globally stable in the algebraic form of t−1/α. 相似文献
64.
Jean-Michel Roquejoffre Violaine Roussier-Michon 《Annali di Matematica Pura ed Applicata》2009,188(2):207-233
Bistable reaction–diffusion equations are known to admit one-dimensional travelling waves which are globally stable to one-dimensional
perturbations—Fife and McLeod [7]. These planar waves are also stable to two-dimensional perturbations—Xin [30], Levermore-Xin
[19], Kapitula [16]—provided that these perturbations decay, in the direction transverse to the wave, in an integrable fashion.
In this paper, we first prove that this result breaks down when the integrability condition is removed, and we exhibit a large-time
dynamics similar to that of the heat equation. We then apply this result to the study of the large-time behaviour of conical-shaped
fronts in the plane, and exhibit cases where the dynamics is given by that of two advection–diffusion equations.
相似文献
65.
ZENG HuiHui 《中国科学 数学(英文版)》2014,(2)
This paper studies the multidimensional stability of traveling fronts in monostable reaction-difusion equations,including Ginzburg-Landau equations and Fisher-KPP equations.Eckmann and Wayne(1994)showed a one-dimensional stability result of traveling fronts with speeds c c(the critical speed)under complex perturbations.In the present work,we prove that these traveling fronts are also asymptotically stable subject to complex perturbations in multiple space dimensions(n=2,3),employing weighted energy methods. 相似文献
66.
本文研究了一些拟线性Burgers型方程的波前解的存在性、稳定性,利用谱分析的方法,证明了光滑波前解在某些加权空间中的渐近稳定性。 相似文献
67.
The effects of a complexing agent on travelling waves in autocatalytic systems with applied electric fields 总被引:2,自引:0,他引:2
The effects of electric fields on the reaction fronts that arisein a system governed by an autocatalytic reaction and a complexationreaction between the autocatalyst and a complexing agent areconsidered. The complexation reaction is assumed to be fastrelative to the autocatalytic reaction and the equations forthis limit are derived. The corresponding travelling waves arediscussed, the case of quadratic autocatalysis being treatedin detail. The existence of minimum speed waves is examined,being dependent on the ratio of diffusion coefficients D, theconcentration S0 and equilibrium constant K of the complexationreaction as well as the electric field strength E. It is seenthat, for some parameter values, minimum speed waves have negativeautocatalayst concentrations, and waves which have the lowestspeed consistent with non-negative concentrations are also obtained.Numerical integrations of the initial-value problem are performedfor representative parameter values. These show the developmentof the appropriate travelling wave (when it exists) as the largetime behaviour of the system, and, in cases where no travellingwave exists, the numerical integrations show the electrophoreticseparation of substrate and autocatalyst. 相似文献
68.
Grégory Faye Matt Holzer 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(2):545-584
We study invasion fronts and spreading speeds in two component reaction–diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the existence of a bifurcation to locked fronts where both components invade at the same speed. Expansions of the wave speed as a function of the diffusion constant of one species are obtained. The bifurcation can be sub or super-critical depending on whether the locked fronts exist for parameter values above or below the bifurcation value. Interestingly, in the sub-critical case numerical simulations reveal that the spreading speed of the PDE system does not depend continuously on the coefficient of diffusion. 相似文献
69.
Jonathan Goodman Judith R. Miller 《Journal of Dynamics and Differential Equations》1999,11(2):255-277
We prove nonlinear stability in L
1 of planar shock front solutions to a viscous conservation law in two spatial dimensions and obtain an expression for the asymptotic form of small perturbations. The leading-order behavior is shown rigorously to be governed by an effective diffusion coefficient depending on forces transverse to the shock front. The proof is based on a spectral analysis of the linearized problem. 相似文献
70.
Summary Certain problems in optical scattering are best understood when the more complicated exact scattering theory is replaced by
an approximation. The Fraunhofer approximation is a well-known example. In the past ten years a considerable amount of work
has been done in various disciplines towards assessing the usefulness of a new approximation referred to in the literature
either as the eikonal approximation or as the high-energy approximation. The purpose of this paper is to provide a much needed
review of this work and in addition to examine the historical evolution of this approximation which essentially started in
optics when Bruns introduced the term eikonal in 1895.
Part of this work was done when SKS was at Saha Institute of Nuclear Physics, Calcutta, and at Institute of Wetland Management
and Ecological Design, Calcutta, India. 相似文献