Asymptotic Behavior at Infinity of the Dirichlet Problem Solution of the 2k Order Equation in a Layer
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https://elib.sfu-kras.ru/handle/2311/13269Author:
Kildyushov, Mikhail S.
Nikishkin, Valery A.
Кильдюшов, Михаил С.
Никишкин, Валерий А.
Date:
2014-07Abstract:
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 Для оператора (− )ku(x) + 2ku(x) в Rn (n > 2, k > 2) получен явный вид фундаментального
решения, а для уравнения (− )ku(x)+ 2ku(x) = f(x) (с финитной бесконечно дифференцируемой
функцией f ) первый член асимптотики решения на бесконечности. Изучается также задача
Дирихле в слое из Rn+1
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