Deduction of limit equations for elliptic problems in thin domains by means of electronic computers. (Russian) Zbl 0626.65129

Let \(\Omega\) be a bounded region in \(R^{n-1}\) with a smooth boundary \(\partial \Omega\), \(Q_ h=\Omega \times (-h,h),\) \(Q_ h\subseteq R^ n\), \(h\to 0\). Boundary value problems for strongly elliptic symmetric systems of the second order are considered in \(Q_ h\). Dirichlet conditions are given on \(\partial \Omega \times (-h,h)\), natural boundary conditions on the planes \(x_ n=\pm h\). Asymptotic expansions of solutions are analyzed. The coefficients of the limit systems are defined from boundary value problems for ordinary differential equations. Iterations with analytical representations of the coefficients can be done on a computer. Examples for the Poisson equation and systems from the elasticity theory are included.
Reviewer: E.D’yakonov


65Z05 Applications to the sciences
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
74B10 Linear elasticity with initial stresses