Translator Disclaimer
November/December 2010 Vector-valued heat equations and networks with coupled dynamic boundary conditions
Delio Mugnolo
Adv. Differential Equations 15(11/12): 1125-1160 (November/December 2010).

Abstract

Motivated by diffusion processes on metric graphs and ramified spaces, we consider an abstract setting for interface problems with coupled dynamic boundary conditions belonging to a quite general class. Beside well posedness, we discuss positivity, $L^\infty$-contractivity and further invariance properties. We show that the parabolic problem with dynamic boundary conditions enjoys these properties if and only if its counterpart with time-independent boundary conditions does also. Furthermore, we prove continuous dependence of the solution to the parabolic problem on the boundary conditions in the considered class.

Citation

Download Citation

Delio Mugnolo. "Vector-valued heat equations and networks with coupled dynamic boundary conditions." Adv. Differential Equations 15 (11/12) 1125 - 1160, November/December 2010.

Information

Published: November/December 2010
First available in Project Euclid: 18 December 2012

zbMATH: 1226.47046
MathSciNet: MR2743497

Subjects:
Primary: 35K50, 47D06

Rights: Copyright © 2010 Khayyam Publishing, Inc.

JOURNAL ARTICLE
36 PAGES


SHARE
Vol.15 • No. 11/12 • November/December 2010
Back to Top