Asymptotic properties of solutions of semilinear second-order elliptic equations in cylindrical domains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

Asymptotic properties of solutions of semilinear second-order elliptic equations in cylindrical domains

Authors:

V. A. Kondratiev

Abstract:

The equations under consideration have the following structure:

$frac{{partial ^2 u}}{{partial x_n^2 }} + sumlimits_{i,j = 1}^{n - 1} {frac{partial }{{partial x_i }}left( {a_{ij} (x)frac{{partial u}}{{partial x_j }}} right)} + sumlimits_{i = 1}^{n - 1} {a_i (x)frac{{partial u}}{{partial x_i }}} - f(u,x_n ) = 0,$

where 0 < x _n < ∞, (x ₁, …, x _n−1) ∈ Ω, Ω is a bounded Lipschitz domain, $f(0,x_n ) equiv 0,tfrac{{partial f}}{{partial u}}(0,x_n ) equiv 0$ is a function that is continuous and monotonic with respect to u, and all coefficients are bounded measurable functions. Asymptotic formulas are established for solutions of such equations as x _n → + ∞; the solutions are assumed to satisfy zero Dirichlet or Neumann boundary conditions on ∂Ω. Previously, such formulas were obtained in the case of a _ij, a_i depending only on (x ₁, …, x _n−1). __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 98–111, 2005.

Keywords:

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