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On the Asymptotic Behaviour of Some Nonlinear Parabolic Systems
Mahmoud M. El-Borai ...et al KYUNGPOOK UNIVERSITY 1997 Kyungpook mathematical journal Vol.37 No.1
We study the existence and uniqueness and asymptotic behaviour of the solutions of the Cauchy problem for some non-linear parabolic systems of the form. ◁수식삽입▷(원문을 참조하세요) x ∈ Rⁿ^(n) , u , f_(i) ∈ R^(υ) , i = 1, 2, 3, where Rⁿ is the n-dimensional Euclidean space and (A_(α), |α|≤ 2m) is a family of square matrices whose elements are suffciently smooth functions on Rⁿ ×[0, ∞). It is supposed that f₁(x, t, 0) = 0 and f₃(x, t, u) ≤Θ(t) for all x ∈ Rⁿ, t ∈ [0, ∞), |u| < M; whereΘ(t) ∈ L₁[0, ∞). The considered problem is solved under a suitable condition on f₂ by using Liapunov function.