【摘要】 <正>应用上常常提出由不同类型的方程式耦合而成的方程组,其中许多是拟线性退缩方程组。本文考虑如下形式的耦合较强的（有未知函数的导数参加耦合）拟线性退缩方程组 a/ax_i(α^ij（u,t,x）au/ax_i)+ab₁ⁱ（u,v,t,x）/ax_i+c₁（u,v,t,x）=0 （1） av/at+ab₂ⁱ（v,t,x）/ax_i+c₂（u,v,t,x）=0, （2） （重复指标表示从1到n求和,下同）其中α^ij（u,t,x）在R¹×_T（_T=（0,T）×Ω,ΩR_n为一有界域,其边界Ω适当光滑）上有界且满足一致椭圆性条件α^ij（u,t,x）ξ_iξ_j≥μ₀|ξ|²（ξ=（ξ₁,…,ξ_n）∈R_n,μ₀>为常数）。方程组（1）、（2）与文[1]中提到的渗流方程组有某些类似。更多还原

【Abstract】 In the region is a bounded region with an appropriately smooth boundary (?)θ) we consider the coupled system (1) (2)in which the copling is concerned with the first order derivatives of the unknown functions. The initial-boundary conditions are given by ( 3 ) (4)We assume that the equation (1) is strictly elliptic, i. e., the coefficients satisfy the condition where μ0>0 is a constant.We investigate the solvability of the initial-boundary value problem (l) - (4)in a class of all pairs of functions (u,v) with μ(t, ·) W1/2(Ω) a. e. on [0,T] and on[o,T]. For any given ,we first solve the boundary value problem (l), (3) for u. Then substituting u to the equation (2) and solving the initial-boundary value problem (2), (4), we obtain a function v. Thus an operate p from L1 (QT) into itself is defined. Under certain assumptions on the coefficients of (1) , (2) , by means of the Schauder fixed point theorem we prove that p has at least one fixed point in L1 (QT) .As a consequence, the existence of solutions of the problem (1) - (4) is established.更多还原