Monotone method and periodic solution of non linear parabolic boundary value problem for systems

Publisher: Cambridge University Press

E-ISSN: 1755-1633|29|2|231-242

ISSN: 0004-9727

Source: Bulletin of the Australian Mathematical Society, Vol.29, Iss.2, 1984-04, pp. : 231-242

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Abstract

A system of parabolic equations is considered: Lui = uituix = fi (x, t, u, uix) on Q, Biui(j, t) = ωij(t), t (−∞, ∞), j = 0, 1, i = 1, 2, …, n, where Bi is one of the boundary operators Biui = ui or Biui = ∂ui/∂v + βi(x, t)ui, x = 0, 1, Ω = (0, 1), Q = Ω × R, u(=(u1, …, un)): QRn, v(x) is the outward normal to the boundary ∂Ω, f, u, ω0, ω1 are n-valued functions and f, ω0, ω1 are periodic in t with period T and Bi is a positive function.