On the well-posedness of evolutionary equations on infinite graphs. (English) Zbl 1306.47032
Arendt, Wolfgang (ed.) et al., Spectral theory, mathematical system theory, evolution equations, differential and difference equations. Selected papers of 21st international workshop on operator theory and applications, IWOTA10, Berlin, Germany, July 12–16, 2010. Basel: Birkhäuser (ISBN 978-3-0348-0296-3/hbk; 978-3-0348-0297-0/ebook). Operator Theory: Advances and Applications 221, 653-666 (2012).
The purpose of this paper is to present a unified approach for obtaining well-posedness of various evolution equations on (finite or infinite) graphs in a Hilbert space setting. The authors rely on a general structural result on evolution equations in mathematical physics proved in [R. Picard, Math. Methods Appl. Sci. 32, No. 14, 1768–1803 (2009; Zbl 1200.35050)]. The main issue is to obtain a skew-selfadjoint realisation of the respective spacial operators, and the authors classify this in terms of the appropriate boundary conditions on graphs. Transport, wave, and heat equations are presented as examples (possibly including delay terms).
For the entire collection see [Zbl 1245.47001].
For the entire collection see [Zbl 1245.47001].
Reviewer: Marjeta Kramar Fijavž (Ljubljana)
MSC:
| 47B25 | Linear symmetric and selfadjoint operators (unbounded) |
| 35R03 | PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. |
| 58D25 | Equations in function spaces; evolution equations |
Citations:
Zbl 1200.35050References:
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