Advances in Differential Equations

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

Delio Mugnolo

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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.

Article information

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

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854437

Mathematical Reviews number (MathSciNet)
MR2743497

Zentralblatt MATH identifier
1226.47046

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

Citation

Mugnolo, Delio. Vector-valued heat equations and networks with coupled dynamic boundary conditions. Adv. Differential Equations 15 (2010), no. 11/12, 1125--1160. https://projecteuclid.org/euclid.ade/1355854437.


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