一类含时滞反应扩散方程波前解的存在性

Existence of Wave Front Solutions of a Kind of Reaction-diffusive Equations with Delays

利用J.Wu和X.Zou(J.Dynam.Diff.Eqns.,2001,13(3):651～687.)建立的解的存在性理论,研究 2u1(x,t) u1(x,t) t=D1b1+a1u2(x,t-τ2)], x2+r1u1(x,t)[1-u1(x,t-τ1) u2(x,t) 2u2(x,t) t=D2b2+a2u1(x,t-τ4)], x2+r2u2(x,t)[1-u2(x,t-τ3)的行波解,其中x∈R,t∈R,ui(x,t)∈R,Di>0,ri>0,ai>0,bi>0,i=1,2,a1a2<1,τj>0,j=1,2,3,4,得到了这个系统波前解存在的充分条件.

Using the theory developed by J. Wu and X. Zou(J. Dynam. Diff. Eqns.,2001,13(3):651～687.), this paper studied travelling wave solutions of the reaction-diffusive equationsu_1(x,t)t=D_1~2u_1(x,t)x^2+r_1u_1(x,t)[1-u_1(x,t-τ_1)b_1+a_1u_2(x,t-τ_2)],u_2(x,t)t=D_2~2u_2(x,t)x^2+r_2u_2(x,t)[1-u_2(x,t-τ_3)b_2+a_2u_1(x,t-τ_4)],where x∈R,t∈R,u_i(x,t)∈R,D_i>0,r_i>0,a_i>0,b_i>0,i=1,2,a_1a_2<1,τ_j>j=1,2,3,4, and a sufficient condition for the existence of wave front solution is obtained for this system.