Journal of Siberian Federal University. Mathematics & Physics / Asymptotic Behavior at Infinity of the Dirichlet Problem Solution of the 2k Order Equation in a Layer

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2014 7 (3)
Authors
Kildyushov, Mikhail S.; Nikishkin, Valery A.
Contact information
Kildyushov, Mikhail S.:Institute of Computer Technology, Moscow State University of Economics, Statistics and Informatics, Nezhinskaya, 7, Moscow, 119501 Russia;; Nikishkin, Valery A.:Institute of Computer Technology, Moscow State University of Economics, Statistics and Informatics, Nezhinskaya, 7, Moscow, 119501 Russia;
Keywords
asymptotic behavior; elliptic equation; fundamental solution; estimation of solution; G-Meyer function
Abstract

For the operator (− )ku(x) + 2ku(x) with x 2 Rn(n > 2, k > 2) an explicit fundamental solution is obtained, and for the equation (− )ku(x) + 2ku(x) = f(x) (for f 2 C1(Rn) with compact support) the leading term of an asymptotic expansion at infinity of a solution is computed. The same result is obtained for the solution of the Dirichlet problem in a layer in Rn+1

Pages
311–317
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/13269