【摘要】 <正> 在不少文章(如[1],[2],[3])中,对扩散反应方程的定解问题建立了比较原理,通过比较函数得到解的存在性、解的估计及t→+∞时解的极限性质。 本文考察如下扩散反应方程的定解问题更多还原

【Abstract】 In the present paper we study the asymptotic behavior of the positive solutions of the equation:Satisfying the boundary condition and initial condition:where u = (u1(x, t), u2(x, t), u3(x, t)) and F(u) = (F1(u), F2(u), F3(u)),aii<0, aij≥0 (i≡j), bi being constants. It is assumed that Ω is a bounded domain in Rn, with a boundary surface Ω of class C2+α for some α ∈ (0, 1) and u0(x) is Holder continuous on Ω.Our main result is the following.Theorem. Suppose that the following conditions are satisfied:1° The matrix A = (aij)3×3 has a path of nonsigularity.2° bi>0 (i = 1, 2, 3).3° There exists a unique solution u* of F(u) = 0 with u*∈ R+3.4° Ai1 +Ai2 +Ai3>0 (i=1, 2, 3), Aij being the algebraic cofactors of det A, det A<0 or A = 1/2(A + AT) is negatively definite.5° u0(x) = (u01(x), u02(x), u03(x))≥0, u0i(x)≡0 (i = 1, 2, 3). Then there exists a unique positive solution u(x, t) with更多还原