【摘要】 研究一类时滞广义Logistic反应扩散方程 u t(x,t)=D 2u x2(x,t)+u(x,t)(a+bup(x,t-τ)-cuq(x,t-τ))的波前解.其中,x∈R,t≥0,D,a,c∈(0,∞),b∈R,p,q∈[1,∞),p<q.利用J.Wu和X.Zou(J.Dy nam.Diff.Eqns.,2001,13(3):651～687.)建立的思想,通过构造合适的上、下解,证明了当时滞τ充分小时,该方程波前解的存在性.更多还原

【Abstract】 In this paper, a generalized Logistic reaction-diffusion equation with delay:ut(x,t)=D~2ux~2(x,t)+u(x,t)(a+bu~p(x,t-τ)-cu~q(x,t-τ)),(x∈R,t≥0,D,a,c∈(0,∞),b∈R,p,q∈[1,∞),p<q) is considered. The existence of traveling wave fronts solutions is proved when the delay τ is sufficietly small by using the technique developed by J. Wu and X. Zou (J. Dynam. Diff. Eqns.,2001,13(3):651～687.) and constructing a proper upper and a lower solution.更多还原