Conservation laws for multidimensional systems and related linear algebra problems

S. Igonin

Research output: Book/ReportReportOther research output

2 Citations (Scopus)
92 Downloads (Pure)

Abstract

We consider multidimensional systems of PDEs of generalized evolution form with $t$-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order $t$-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model, and the Belousov-Zhabotinskii system. To achieve this, we determine the conditions for a quadratic matrix $A$ with entries from an arbitrary field to be similar (conjugate) to its transpose $A^t$ or to the matrix $-A^t$, which is of independent interest.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Publication statusPublished - 2002

Publication series

Name
PublisherDepartment of Applied Mathematics, University of Twente
No.1626
ISSN (Print)0169-2690

Keywords

  • MSC-15A24
  • MSC-35K57
  • MSC-37K05
  • MSC-37K10
  • IR-65813
  • MSC-76H05
  • EWI-3446

Cite this

Igonin, S. (2002). Conservation laws for multidimensional systems and related linear algebra problems. Enschede: University of Twente, Department of Applied Mathematics.
Igonin, S. / Conservation laws for multidimensional systems and related linear algebra problems. Enschede : University of Twente, Department of Applied Mathematics, 2002.
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Igonin, S 2002, Conservation laws for multidimensional systems and related linear algebra problems. University of Twente, Department of Applied Mathematics, Enschede.

Conservation laws for multidimensional systems and related linear algebra problems. / Igonin, S.

Enschede : University of Twente, Department of Applied Mathematics, 2002.

Research output: Book/ReportReportOther research output

TY - BOOK

T1 - Conservation laws for multidimensional systems and related linear algebra problems

AU - Igonin, S.

N1 - Imported from MEMORANDA

PY - 2002

Y1 - 2002

N2 - We consider multidimensional systems of PDEs of generalized evolution form with $t$-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order $t$-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model, and the Belousov-Zhabotinskii system. To achieve this, we determine the conditions for a quadratic matrix $A$ with entries from an arbitrary field to be similar (conjugate) to its transpose $A^t$ or to the matrix $-A^t$, which is of independent interest.

AB - We consider multidimensional systems of PDEs of generalized evolution form with $t$-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order $t$-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model, and the Belousov-Zhabotinskii system. To achieve this, we determine the conditions for a quadratic matrix $A$ with entries from an arbitrary field to be similar (conjugate) to its transpose $A^t$ or to the matrix $-A^t$, which is of independent interest.

KW - MSC-15A24

KW - MSC-35K57

KW - MSC-37K05

KW - MSC-37K10

KW - IR-65813

KW - MSC-76H05

KW - EWI-3446

M3 - Report

BT - Conservation laws for multidimensional systems and related linear algebra problems

PB - University of Twente, Department of Applied Mathematics

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Igonin S. Conservation laws for multidimensional systems and related linear algebra problems. Enschede: University of Twente, Department of Applied Mathematics, 2002.