Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows

On a Hele-Shaw-Type Domain Evolution with Convected Surface Energy Density

Interest is directed to a moving boundary problem with a gradient flow structure which generalizes surface-tension driven Hele-Shaw flow to the case of nonconstant surface tension coefficient taken along with the liquid particles at the boundary. In the case with kinetic undercooling regularization well-posedness of the resulting evolution problem in Sobolev scales is proved, including cases in...

WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS

Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries

We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets M of Rd endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqu...

Vector-valued Heat Equations and Networks with Coupled Dynamic Boundary Conditions

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∞-contractivity and further invariance properties. We show that the parabolic problem with dynamic boundary conditions enjoy these properties if an...

Nonlinear diffusion: Geodesic Convexity is equivalent to Wasserstein Contraction

It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the space of probability measures equipped with the Euclidean Wasserstein distance. Under suitable convexity conditions on the nonlinearity, due to R. J. McCann [10], the associated entropy is geodesically convex, which implies a contraction type property between all solutions with respect to this dista...