Exact solutions of the inhomogeneous problems for polyparabolic operator
type: Item
instance of: scholarly article
zbMATH Open document ID: 0962.35039
author: Alexander N. Zhukovsky
author: Victor P. Karagodov
publication date: 2001-04-25T00:00:00Z
Mathematics Subject Classification ID: 35E15
Mathematics Subject Classification ID: 35K70
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 35A08
zbMATH DE Number: 1591506
zbMATH Keywords: well-posed problem
MaRDI profile type: Publication
title: Exact solutions of the inhomogeneous problems for polyparabolic operator
review text: The authors consider the equation NEWLINE\[NEWLINE T^{m+1}u\equiv \sum\limits_{j=0}^{m+1}(- 1)^j\binom{m+1}{j}\frac{\partial^{m-j+1}} {\partial t^{m- j+1}} \nabla^{2j}u(t,x)=f(t,x),\quad t>0, x\in \mathbb R^n. \tag{1} NEWLINE\]NEWLINE It is shown that in order to obtain a well-posed problem for the equation (1) the initial data NEWLINE\[NEWLINE (T^ku)(+0,x),\quad k=1,\ldots ,m, NEWLINE\]NEWLINE can be used. A fundamental solution is found explicitly.NEWLINENEWLINEFor the entire collection see [Zbl 0937.00046].
reviewed by: Anatoly N. Kochubei
description: scientific article