Abstract:
A harmonic function is considered in a three-dimensional bounded domain. Its normal derivative is given on nearly the entire boundary of the domain, while the value of the harmonic function is specified on the remaining small portion. The method of matched asymptotic expansions is used to construct a complete uniform asymptotic expansion of the function in powers of a small parameter characterizing the size of the boundary portion with a specified function value. The asymptotic expansion is rigorously substantiated.
Key words:harmonic function, mixed boundary value problem, small parameter, method of matched asymptotic expansions.
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