Travelling Wave Solutions to a Semilinear Diffusion System

Finite travelling waves for semilinear parabolic systems

“…In fact, by the continuation of solutions theory the conclusion (a) is obvious. To prove conclusion (b), let f^z) -f]" = i y™"( z )-Because y^z) > 0 and y\{z) > 0, we have that f-(z) > 0 and there exists f 0 > 0 such that /(z) > / 0 for all z > 1 and 1 < i < n. By (2) we have If c = 0, then we have y\(z) > as z ->• +oo, 1 < i < n.…”

“…Finite travelling waves of semilinear parabolic systems (1) were first studied by J. Esquinas and M. A. Herrero in [2] for the case « = 2 and m ll =m 22 = 0, d x -d 2 -e i =e 1 = \ by using the theory of integral equations and the Schauder fixed point theorem.…”

Backward Blow-up Estimates and Initial Trace for a Parabolic System of Reaction-Diffusion

“…Some existence results are given in [12] for bounded initial data, and then in [3] for more general multipower systems with non smooth data, see also [13] for quasilinear operators. Otherwise the existence of traveling waves is treated in [9]. For the associated elliptic system −∆u + v p = 0, −∆v + u q = 0, (1.4) the isolated singularities are completely described in [4] for the superlinear case pq > 1 and for the sublinear case pq < 1, see also [17], [18] for p, q ≧ 1.…”