Existence of an extinction wave in the Fisher equation with a shifting habitat

Abstract

This paper deals with the existence of traveling wave solutions of the Fisher equation with a shifting habitat representing a transition to a devastating environment. By constructing a pair of appropriate upper/lower solutions and using the method of monotone iteration, we prove that for any given speed of the shifting habitat edge, this reaction-diffusion equation admits a monotone traveling wave solution with the speed agreeing to the habitat shifting speed, which accounts for an extinction wave. This predicts not only how fast but also in what manner a biological species will die out in such a shifting habitat.

Spatial Dynamics of a Nonlocal Dispersal Population Model in a Shifting Environment

“…Recall that c > 0 is the habitat shifting speed. As explained in [12], we impose the following boundary conditions In the following, by the combination of super/sub-solutions and monotone iterations, we will prove that (4.3) admits a nonincreasing solution satisfying (4.4) for any given c > 0, which gives rise to the nondecreasing traveling wave solution of (1.1) connecting 0 to r(∞).…”

Association of Jensen’s inequality for s-convex function with Csiszár divergence

“…for all ξ i ∈ I and α i ≥ 0 with n i=1 α i = 1. Convex function has wide applications in pure and applied mathematics, physics, and other natural sciences [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]; it has many important and interesting properties [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] such as monotonicity, continuity, and differentiability. Recently, many generalizations and extensions have been made for the convexity, for example, s-convexity [38], strong convexity [39][40][41], preinvexity [42], GA-convexity [43], GG-convexity [44], Schur convexity [45][46][47][48]…”

Stability of antiperiodic recurrent neural networks with multiproportional delays

“…Remark To the author's knowledge, the issue of antiperiodic RNNs involving proportional delays has never been investigated. Obviously, the corresponding conclusions in Shao, Tan, Gong, Cao, Li, Zhou, Yang, Wang, Peng and Wang, Cai et al, Li et al, Kudu, Hu et al, Hu and Zou, Huang et al, and Hu et al and the references cited therein cannot be used to deal with the exponential convergence on the antiperiodic phenomenon for system .…”