Browsing by Author "Solar, Abraham"

Now showing 1 - 5 of 5
  • No Thumbnail Available
    Item
    A simple approach to the wave uniqueness problem
    (2019) Solar, Abraham; Trofimchuk, Sergei
    We propose a new approach for proving uniqueness of semi-wavefronts in generally non-monotone monostable reaction-diffusion equations with distributed delay. This allows to solve an open problem concerning the uniqueness of non-monotone (hence, slowly oscillating) semi-wavefronts to the KPP-Fisher equation with delay. Similarly, a broad family of the Mackey-Glass type diffusive equations is shown to possess a unique (up to translation) semi-wavefront for each admissible speed. (C) 2018 Elsevier Inc. All rights reserved.
  • Thumbnail Image
    Item
    An estimation of level sets for non local KPP equations with delay
    (2019) Benguria Donoso, Rafael; Solar, Abraham
  • No Thumbnail Available
    Item
    AN ITERATIVE ESTIMATION FOR DISTURBANCES OF SEMI-WAVEFRONTS TO THE DELAYED FISHER-KPP EQUATION
    (2019) Benguria, Rafael D.; Solar, Abraham
    We give an iterative method to estimate the disturbance of semi-wavefronts of the equation (u) over dot (t, x) = u '' (t, x) + u(t, x)(1 - u(t - h, x)), x is an element of R, t > 0, where h > 0. As a consequence, we show the exponential stability, with an unbounded weight, of semi- wavefronts with speed c >= 2 v 2 and h > 0. Under the same restriction of c and h, the uniqueness of semi- wavefronts is obtained.
  • No Thumbnail Available
    Item
    STABILITY OF NON-MONOTONE AND BACKWARD WAVES FOR DELAY NON-LOCAL REACTION-DIFFUSION EQUATIONS
    (2019) Solar, Abraham
    This paper deals with the stability of semi-wavefronts to the follRowing delay non-local monostable equation: (v) over dot(t, x) = Delta v(t, x) - v(t, x) + integral(Rd) K(y)g(v(t - h, x - y))dy, x is an element of R-d, t > 0; where h > 0 and d is an element of Z(+). We give two general results for d >= 1: on the global stability of semi-wavefronts in L-p-spaces with unbounded weights and the local stability of planar wavefronts in L-p-spaces with bounded weights. We also give a global stability result for d = 1 which yields to the global stability in Sobolev spaces with bounded weights. Here g is not assumed to be monotone and the kernel K is not assumed to be symmetric, therefore non-monotone semi-wavefronts and backward semiwavefronts appear for which we show their stability. In particular, the global stability of critical wavefronts is stated.
  • No Thumbnail Available
    Item
    Stability of semi-wavefronts for delayed reaction-diffusion equations
    (2019) Solar, Abraham
    This paper deals with the asymptotic behavior of solutions to the delayed monostable equation: (*) u(t)(t, x) = u(xx)(t, x)-u(t, x)+g(u(t-h, x)), x is an element of R, t > 0; here h > 0 and the reaction term g : R+ -> R+ is Lipschitz continuous and has exactly two fixed points (zero and kappa > 0). Under certain condition on the derivative of g at kappa (without assuming classic KPP condition for g) the global stability of fast semi-wavefronts is proved. Also, when the Lipschitz constant L-g is equal to g'(0) the stability of all semi-wavefronts (e.g., critical, non-critical and asymptotically periodic semi-wavefronts) on each interval in the form (-infinity, N], N is an element of R, to (*) is established, which includes classic equations such as the Nicholson's model.