Qualitative properties of nonlinear parabolic operators II: the case of PDE systems

József Csóka, I. Faragó, Róbert Horváth, J. Karátson, Sergey Korotov

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The solution of a parabolic problem is expected to reproduce the basic qualitative properties of the original phenomenon, such as nonnegativity/nonpositivity preservation, maximum/minimum principles and maximum norm contractivity, without which the model might lead to unrealistic quantities in conflict with physical reality. This paper presents characterizations of qualitative properties for a general class of nonlinear parabolic systems. This is a continuation of the authors’ research, published in a previous paper in this journal on scalar equations. Cooperativity of the systems plays an essential role in most of the results.

Original languageEnglish
Pages (from-to)64-86
Number of pages23
JournalJournal of Mathematical Analysis and Applications
Volume468
Issue number1
DOIs
Publication statusPublished - Dec 1 2018

Fingerprint

Parabolic Operator
Qualitative Properties
Nonlinear Operator
Nonlinear Parabolic Systems
Contractivity
Minimum Principle
Maximum Norm
Nonnegativity
Parabolic Problems
Preservation
Continuation
Scalar
Model
Conflict
Class

Keywords

  • Maximum/minimum principles
  • Nonnegativity/nonpositivity preservation
  • Parabolic PDEs
  • Qualitative properties

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Qualitative properties of nonlinear parabolic operators II : the case of PDE systems. / Csóka, József; Faragó, I.; Horváth, Róbert; Karátson, J.; Korotov, Sergey.

In: Journal of Mathematical Analysis and Applications, Vol. 468, No. 1, 01.12.2018, p. 64-86.

Research output: Contribution to journalArticle

@article{8996b61b89d740bb9c56d5f0eec6713e,
title = "Qualitative properties of nonlinear parabolic operators II: the case of PDE systems",
abstract = "The solution of a parabolic problem is expected to reproduce the basic qualitative properties of the original phenomenon, such as nonnegativity/nonpositivity preservation, maximum/minimum principles and maximum norm contractivity, without which the model might lead to unrealistic quantities in conflict with physical reality. This paper presents characterizations of qualitative properties for a general class of nonlinear parabolic systems. This is a continuation of the authors’ research, published in a previous paper in this journal on scalar equations. Cooperativity of the systems plays an essential role in most of the results.",
keywords = "Maximum/minimum principles, Nonnegativity/nonpositivity preservation, Parabolic PDEs, Qualitative properties",
author = "J{\'o}zsef Cs{\'o}ka and I. Farag{\'o} and R{\'o}bert Horv{\'a}th and J. Kar{\'a}tson and Sergey Korotov",
year = "2018",
month = "12",
day = "1",
doi = "10.1016/j.jmaa.2018.07.015",
language = "English",
volume = "468",
pages = "64--86",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - Qualitative properties of nonlinear parabolic operators II

T2 - the case of PDE systems

AU - Csóka, József

AU - Faragó, I.

AU - Horváth, Róbert

AU - Karátson, J.

AU - Korotov, Sergey

PY - 2018/12/1

Y1 - 2018/12/1

N2 - The solution of a parabolic problem is expected to reproduce the basic qualitative properties of the original phenomenon, such as nonnegativity/nonpositivity preservation, maximum/minimum principles and maximum norm contractivity, without which the model might lead to unrealistic quantities in conflict with physical reality. This paper presents characterizations of qualitative properties for a general class of nonlinear parabolic systems. This is a continuation of the authors’ research, published in a previous paper in this journal on scalar equations. Cooperativity of the systems plays an essential role in most of the results.

AB - The solution of a parabolic problem is expected to reproduce the basic qualitative properties of the original phenomenon, such as nonnegativity/nonpositivity preservation, maximum/minimum principles and maximum norm contractivity, without which the model might lead to unrealistic quantities in conflict with physical reality. This paper presents characterizations of qualitative properties for a general class of nonlinear parabolic systems. This is a continuation of the authors’ research, published in a previous paper in this journal on scalar equations. Cooperativity of the systems plays an essential role in most of the results.

KW - Maximum/minimum principles

KW - Nonnegativity/nonpositivity preservation

KW - Parabolic PDEs

KW - Qualitative properties

UR - http://www.scopus.com/inward/record.url?scp=85051630563&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051630563&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2018.07.015

DO - 10.1016/j.jmaa.2018.07.015

M3 - Article

AN - SCOPUS:85051630563

VL - 468

SP - 64

EP - 86

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -