On abstract grad-div systems

Rainer Picard, Stefan Seilder, Sascha Trostorff, Marcus Waurick

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10 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)4888-4917
Number of pages30
JournalJournal of Differential Equations
Issue number6
Early online date7 Dec 2015
Publication statusPublished - 15 Mar 2016


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  • Gelfand triples
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  • dynamic boundary conditions
  • Leontovich boundary condition


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