14 citations · 41 across the 22 of their papers we have counts for
25 papers · 1 filter
Mosco convergence framework for singular limits of gradient flows on Hilbert spaces with applications
Yoshikazu Giga, Michał Łasica, Piotr Rybka
We consider the question of convergence of a sequence of gradient flows defined on different Hilbert spaces. In order to give meaning to this idea, we introduce a notion of connect…
The heat equation with the dynamic boundary condition as a singular limit of problems degenerating at the boundary
Yoshikazu Giga, Michał Łasica, Piotr Rybka
We derive the dynamic boundary condition for the heat equation as a limit of boundary layer problems. We study convergence of their weak and strong solutions as the width of the la…
Convergence of solutions to a convective Cahn-Hilliard type equation of the sixth order in case of small deposition rates
Piotr Rybka, Glen Wheeler
We show stabilisation of solutions to the sixth-order convective Cahn-Hilliard equation. {The problem} has the structure of a gradient flow perturbed by a quadratic destabilising t…
The Free Material Design problem for stationary heat equation on low dimensional structures
Tomasz Lewiński, Piotr Rybka, Anna Zatorska-Goldstein
For a given balanced distribution of heat sources and sinks, , we find an optimal conductivity tensor field, , minimizing the thermal compliance. We present in…
The planar Least Gradient problem in convex domains: the discontinuous case
Piotr Rybka, Ahmad Sabra
We study the two dimensional least gradient problem in convex polygonal sets in the plane, . We show the existence of solutions when the boundary data are attained in the tr…
Existence of solutions to a class of variational problems with linear growth on convex domains
Michał Łasica, Piotr Rybka
We consider a class of convex integral functionals composed of a term of linear growth in the gradient of the argument, and a fidelity term involving distance from a datum. S…