On abstract grad-div systems

Rainer Picard, Stefan Seilder, Sascha Trostorff, Marcus Waurick

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

For a large class of dynamical problems from mathematical physics the skew-selfadjointness of a spatial operator of the form ⁎A=(0−C⁎C0), where C:D(C)⊆H0→H1 is a closed densely defined linear operator between Hilbert spaces H0,H1, is a typical property. Guided by the standard example, where C=grad=(∂1⋮∂n) (and ⁎−C⁎=div, subject to suitable boundary constraints), an abstract class of operators C=(C1⋮Cn) is introduced (hence the title). As a particular application we consider a non-standard coupling mechanism and the incorporation of diffusive boundary conditions both modeled by setting associated with a skew-selfadjoint spatial operator A.
LanguageEnglish
Pages4888-4917
Number of pages30
JournalJournal of Differential Equations
Volume260
Issue number6
Early online date7 Dec 2015
DOIs
Publication statusPublished - 15 Mar 2016

Fingerprint

Hilbert spaces
Mathematical operators
Physics
Boundary conditions
Skew
Operator
Self-adjointness
Linear Operator
Hilbert space
Closed
Class

Keywords

  • evolutionary equations
  • Gelfand triples
  • Guyer–Krumhansl heat conduction
  • dynamic boundary conditions
  • Leontovich boundary condition

Cite this

Picard, Rainer ; Seilder, Stefan ; Trostorff, Sascha ; Waurick, Marcus. / On abstract grad-div systems. In: Journal of Differential Equations. 2016 ; Vol. 260, No. 6. pp. 4888-4917.
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abstract = "For a large class of dynamical problems from mathematical physics the skew-selfadjointness of a spatial operator of the form ⁎A=(0−C⁎C0), where C:D(C)⊆H0→H1 is a closed densely defined linear operator between Hilbert spaces H0,H1, is a typical property. Guided by the standard example, where C=grad=(∂1⋮∂n) (and ⁎−C⁎=div, subject to suitable boundary constraints), an abstract class of operators C=(C1⋮Cn) is introduced (hence the title). As a particular application we consider a non-standard coupling mechanism and the incorporation of diffusive boundary conditions both modeled by setting associated with a skew-selfadjoint spatial operator A.",
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On abstract grad-div systems. / Picard, Rainer; Seilder, Stefan; Trostorff, Sascha; Waurick, Marcus.

In: Journal of Differential Equations, Vol. 260, No. 6, 15.03.2016, p. 4888-4917.

Research output: Contribution to journalArticle

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