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
Delio Mugnolo. "Vector-valued heat equations and networks with coupled dynamic boundary conditions." Adv. Differential Equations 15 (11/12) 1125 - 1160, November/December 2010. https://doi.org/10.57262/ade/1355854437
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