Regularity of a Parabolic Differential Equation on Graphs

Bojan Žugec ()
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Bojan Žugec: Faculty of Organization and Informatics, University of Zagreb, 42000 Varaždin, Croatia

Mathematics, 2023, vol. 11, issue 21, 1-10

Abstract: In this paper, motivated by a biodegradable stent problem, we consider a parabolic differential equation on graphs. This kind of equation describes the stent material degradation in time. Since stents are mesh-like structures with thin struts, they can be modelled using a simple structure called the one-dimensional curved rod model. In this way, we obtain a graph-like domain for our parabolic equation. Here, we prove the regularity estimate for the unique solution of the equation, together with corresponding estimates.

Keywords: regularity; parabolic differential equations; graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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