On the Cauchy problem of odd order equation with multiple characteritics
type: Item
instance of: scholarly article
zbMATH Open document ID: 0973.35059
author: S. Abdinazarov
author: O. T. Kurbanov
publication date: 2001-09-24T00:00:00Z
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 35A08
zbMATH DE Number: 1650923
zbMATH Keywords: Airy function
MaRDI profile type: Publication
title: On the Cauchy problem of odd order equation with multiple characteritics
published in: Doklady Akademii Nauk Respubliki Uzbekistan. Matematika, Tekhnicheskie Nauki, Estestvoznanie
review text: The following odd order equation \({\partial^{2n+1}U}/{\partial x^{2n+1}}+(-1)^n \frac{\partial U}{\partial y}=0\) in the domain \(D=\{(x,y)\mid-\infty<x<\infty\), \(y>0\}\) is considered. Using the fundamental solution to the above equation NEWLINE\[NEWLINEV(x-\xi,y-\eta)=(y-\eta)^{-\frac 1{2n+1}}\operatorname {Ain}\left((x-\xi)(y-\eta)^{-\frac 1 {2n+1}}\right),NEWLINE\]NEWLINE where \(\operatorname {Ain}(x)\) denotes the Airy function, the continuity of the solution \(U(x,t)= \int_{-\infty}^{\infty}V(x-\xi,t)\varphi(\xi) d\xi\) for \(t\to+0\) is investigated.
description: scientific article; zbMATH DE number 1650923