Degeneration of semielliptic equations with constant coefficients in rectangular parallelepipeds

Abstract

The paper gives a description of an algorithm of asymptotic expansion in ɛ (ɛ > 0) of the solution u ɛ of the Dirichlet problem for the linear differential semielliptic equation L ɛ u ɛ = h in rectangular parallelepipeds, which contains higher derivatives with a small parameter ɛ. The algorithm is based on the solution of the degenerating as ɛ → 0 Dirichlet problem for the semielliptic equation L 0 u = h of lower order. Some theorems on uniform solvability and regular degeneracy are proved.