On the existence of solution of a system of partial differential equations
type: Item
instance of: scholarly article
title: On the existence of solution of a system of partial differential equations
zbMATH Open document ID: 0809.35002
DOI: 10.4171/ZAA/489
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1994-12-18T00:00:00Z
review text: Summary: Let \(\Pi_ \alpha= \{t\mid 0<\arg t<\alpha\}\) for \(\alpha<\pi\) and denote by \(M\) the class of \(m\)-dimensional vector functions \(u= u(x,t)\) of \(C^ \infty (\mathbb{R}^ n\times \overline{\Pi}_ \alpha)\) analytic in \(t\in \Pi_ \alpha\) and having polynomial growth in \((x,t)\). Let \(A(\xi)\) \((\xi\in \mathbb{R}^ n)\) be a square matrix of order \(m\) with polynomial elements. In the paper we define regularity and strict regularity of the system \(\partial u/\partial t= A(D_ x) u+f\) and prove its solvability in \(M\) for all \(f\in M\).
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35G20
zbMATH DE Number: 704301
zbMATH Keywords: strict regularity
author: A. A. Andriyan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/zaa/489
OpenAlex ID: W2566488255
description: scientific article; zbMATH DE number 704301