Mixed problems for evolution equations
type: Item
instance of: scholarly article
title: Mixed problems for evolution equations
zbMATH Open document ID: 0572.35050
author: Reiko Sakamoto
published in: Journal of Mathematics of Kyoto University
publication date: 1984-01-01T00:00:00Z
review text: Let A(t,x;\(\tau\),\(\xi)\) and \(B_ j(t,x;\tau,\xi)\), \(j=1,2,...,m\), be polynomials with respect to (\(\tau\),\(\xi)\) with coefficients depending on the parameters (t,x). Let us consider a mixed problem (P): \[ A(t,x;D_ t,D_ x)u=f\quad in\quad (0,T)\times {\mathbb{R}}^ n_+, \] \[ B_ j(t,x;D_ t,D_ x)u=g_ j\quad on\quad (0,T)\times \partial {\mathbb{R}}^ n_+,\quad j=1,2,...,m, \] \[ D^ k_ tu=u_ k\quad on\quad \{0\}\times {\mathbb{R}}^ n_+,\quad k=1,2,...,\mu -1, \] where f, \(g_ j\), \(u_ i\) are given. The conditions in terms of the Newton polygon of A are investigated, under which the problem (P) is \(H^{\infty}\)-well posed.
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35R15
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 3912872
zbMATH Keywords: evolution equation
zbMATH Keywords: pseudo-differential operator
zbMATH Keywords: adjoint boundary operator
zbMATH Keywords: mixed problem
zbMATH Keywords: Newton polygon
reviewed by: A. Klíč
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250521276
OpenAlex ID: W4237351146
DOI: 10.1215/KJM/1250521276
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description: scientific article; zbMATH DE number 3912872