14 citations · 41 across the 22 of their papers we have counts for
25 papers
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…