Wavefronts for a cooperative tridiagonal system of differential equations |
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Authors: | D. Hankerson B. Zinner |
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Affiliation: | 1. Department of Discrete and Statistical Sciences, Auburn University, 36849-5307, Auburn, Alabama
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Abstract: | Consider the infinite system of nonlinear differential equations (dot u) n =f(n?1, un, un+1),nε?, wherefεC 1,D 1 f > 0,D 3 f>0, andf(0, 0, 0) = 0 =f(1, 1, 1). Existence of wavefronts—i.e., solutions of the formu n (t) = U(n + ct), wherecε?,U(? ∞) = 0,U(+∞) = 1, andU is strictly increasing—is shown for functionsf which satisfy the condition: there existsa, 0<a<1, such thatf(x, x,x)<0 for 0<x andf(x, x, x) > 0 fora < x < 1. |
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