Abstract:
We consider a harmonic function in a three-dimensional bounded domain. The normal derivative is given on almost the entire boundary, excepting two small sections, on which the value of the function itself is specified. For such a harmonic function, by the method of matching asymptotic expansions, a two-scale asymptotics with respect to a small parameter characterizing the size of the mentioned boundary sections is constructed and justified.
The physical application of the obtained decomposition is given.
Keywords:boundary value problem, Laplace equation, asymptotic expansion, mixed problem, small parameter, matching method, electrical resistance.