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

首页 | 本学科首页

官方微博 | 高级检索

按检索

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:

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

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:

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏