A skin effect approximation for eddy current problems (Q1077635)

Given a simple closed curve \(\Gamma\) in \({\mathbb{R}}^ 2\) with interior domain \(\Omega_-\) and exterior domain \(\Omega_+\), the authors study the following two problems: P(\(\alpha)\): Given \(\alpha >0\), \(a\in {\mathbb{R}}\), \(f\in C(\Gamma)\), \(g\in C(\Gamma)\), find u such that \(\Delta u=\{\alpha^ 2u\) in \(\Omega_-\); \(\Delta u=0\) in \(\Omega_+\); \(u^- =u^++f\) and \(u^-_ n=u^+_ n+g\) on \(\Gamma\) ; u(x)-a log \(| x| =O(1)\) as \(| x| \to \infty.\) P(\(\infty):\) Given \(a\in {\mathbb{R}}\), \(f\in C(\Gamma)\), find u such that \(\Delta u=0\) in \(\Omega_+\); \(u^++f=0\) on \(\Gamma\) ; u(x)-a log \(| x| =O(1)\) as \(| x| \to \infty.\) This paper essentially continuous that of \textit{S. I. Hariharan} and the first author [J. Comp. Phys. 45, 80-89 (1982; Zbl 0478.65080)].