On the behavior of solutions of a semilinear parabolic or elliptic equation satisfying a nonlinear boundary condition in a cylindrical domain期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the behavior of solutions of a semilinear parabolic or elliptic equation satisfying a nonlinear boundary condition in a cylindrical domain

Authors:	I V Filimonova

Abstract:	One considers a semilinear parabolic equation u _t = Lu − a(x)f(u) or an elliptic equation u _tt + Lu − a(x)f(u) = 0 in a semi-infinite cylinder Ω × ℝ₊ with the nonlinear boundary condition $\frac{{\partial u}}{{\partial \nu }} + b(x)g(u) = 0$ , where L is a uniformly elliptic divergent operator in a bounded domain Ω ∈ ℝⁿ; a(x) and b(x) are nonnegative measurable functions in Ω. One studies the asymptotic behavior of solutions of such boundary-value problems for t → ∞. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 368–389, 2007.

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