If time were a graph, what would evolution equations look like?
نویسندگان
چکیده
Linear evolution equations are considered usually for the time variable being defined on an interval where typically initial conditions or time-periodicity of solutions required to single out certain solutions. Here we would like make a point allowing be metric graph network branching points coupling imposed such that can have ramifications and even loops. This not only generalizes classical setting allows more freedom in modeling coupled interacting systems equations, but it also provides unified framework value time-periodic problems. For these time-graph Cauchy problems questions well-posedness regularity parabolic studied along with question which cannot reduced iteratively solvable sequence intervals. Based two different approaches - application Kalton-Weis theorem sum closed operators explicit computation Green's function present main results. We further study some qualitative properties While mainly focus explain how other same lines. is exemplified by discussing constraints non-local akin periodicity.
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ژورنال
عنوان ژورنال: Journal of Evolution Equations
سال: 2021
ISSN: ['1424-3199', '1424-3202']
DOI: https://doi.org/10.1007/s00028-021-00672-8