Existence and Asymptotic Stability of a Stationary Solution of a Singularly Perturbed System of Parabolic Equations in the Case of Intersecting Roots of the Degenerate Equation

摘要

Consider the system of equations ξ~(2)u''= g(u,v,x,ξ), v" = f(u,v,x,ξ), 0 < x < 1, (1) with the boundary conditionsu u'(0,ξ) =u'(1, ξ) = 0, v(O,ξ) = v~O, u(l,ξ)=u~1, (2) where e is a small parameter, 0 ≤ ξ ≤ ξ_0, g ∈ C~2 (Ω-bar),f ∈ C~2 (Ω-bar), Ω = G x [0,ξ_0], G = I_u x D, D = Iv x [0,1], I_u and I_v are some intervals of the variables u and v, and v° and vl are given numbers.