On a certain limit problem for some class of parabolic differential equations of the fourth order
type: Item
instance of: scholarly article
title: On a certain limit problem for some class of parabolic differential equations of the fourth order
zbMATH Open document ID: 0624.35039
author: Jan Musiałek
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 1987-01-01T00:00:00Z
review text: The aim of the paper is a boundary value problem for the equation \(P_ 1P_ 2u(x,t)=f(x,t)\), \(P_ i=D^ 2_ x-C_ iD_ t\) in the strip \(D=\{(x,t):| x| <a\), \(t\in (0,T)\), \(T<\infty \}\), where \(a,C_ i,i=1,2\) are positive constants. The initial conditions are of the form \(P^ i_ 2u(x,0)=f_ i(x)\), \(i=0,1\), the boundary conditions are of the form \(P^ i_ 2u(-a,t)=h_ i(t)\), \(P^ i_ 2u(a,t)=h_ i(t)\), \(i=0,1\). In order to solve this problem suitable Green's functions \(g_ 1,g_ 2\) are used. Existence and uniqueness theorems are given.
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 4013149
zbMATH Keywords: Green's functions
zbMATH Keywords: Existence
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4013149