Existence, uniqueness and stability of weak solutions of parabolic systems with discontinuous nonlinearities
type: Item
instance of: scholarly article
title: Existence, uniqueness and stability of weak solutions of parabolic systems with discontinuous nonlinearities
zbMATH Open document ID: 1173.35519
author: Hideo Deguchi
published in: Monatshefte für Mathematik
publication date: 2009-05-13T00:00:00Z
review text: The paper is devoted to the initial value problem for parabolic systems with discontinuous nonlinearities. First, the authors proof the existence of the maximal or minimal weak solution of the problem in an order interval, by using the upper and lower solution method combined with the monotone iterative technique. Due to the discontinuous nonlinearities, there is no uniqueness of weak solutions of the considered problem for general initial data. This fact is illustrated with an example. Then, the authors prove that certain classes of initial data guarantee the global uniqueness of weak solutions with \(n=2\). In the ending, the authors study the stability of two constant stationary solutions \textbf{0} and \textbf{1}.
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 5553488
zbMATH Keywords: Parabolic systems
zbMATH Keywords: Discontinuous nonlinearities
zbMATH Keywords: initial value problem
zbMATH Keywords: maximal or minimal weak solution
zbMATH Keywords: upper and lower solution method
zbMATH Keywords: monotone iterative technique
zbMATH Keywords: two constant stationary solutions
MaRDI profile type: Publication
full work available at URL: s00605-008-0082-y
OpenAlex ID: W2026128398
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DOI: 10.1007/S00605-008-0082-Y
description: scientific article; zbMATH DE number 5553488