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

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

2009-03-20

arxiv.org/abs/0903.3580v4

(Adv. Diff. Eq. 2010)

Mathematics

Analysis of PDEs

Introduction modified; several bugs fixed; added references; a new example added

Scientific paper

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 enjoy these properties if and only if so does its counterpart with time-independent boundary conditions. Furthermore, we prove continuous dependence of the solution to the parabolic problem on the boundary conditions in the considered class.

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