Well-posedness of non-autonomous transport equation on metric graphs

We consider transport processes on metric graphs with time-dependent velocities and show that, under continuity assumption of the velocity coefficients, the corresponding non-autonomous abstract Cauchy problem is well-posed by means of evolution families and evolution semigroups.

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Bibliographic Details
Published inSemigroup forum Vol. 108; no. 2; pp. 319 - 334
Main Authors Budde, Christian, Kramar Fijavž, Marjeta
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2024
Springer Nature B.V
Subjects
Algebra
Cauchy problems
Evolution
Graphs
Mathematics
Mathematics and Statistics
Research Article
Transport equations
Well posed problems
Transport equation
Evolution semigroups
Non-autonomous problems
Evolution families
Metric graphs
Extrapolation spaces
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Summary:We consider transport processes on metric graphs with time-dependent velocities and show that, under continuity assumption of the velocity coefficients, the corresponding non-autonomous abstract Cauchy problem is well-posed by means of evolution families and evolution semigroups.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-024-10417-x