Advances in Differential Equations

Vector-valued heat equations and networks with coupled dynamic boundary conditions

Delio Mugnolo

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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.

Article information

Adv. Differential Equations, Volume 15, Number 11/12 (2010), 1125-1160.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 35K50


Mugnolo, Delio. Vector-valued heat equations and networks with coupled dynamic boundary conditions. Adv. Differential Equations 15 (2010), no. 11/12, 1125--1160.

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