341 citations · 567 across the 13 of their papers we have counts for
16 papers
A partial uniqueness result and an asymptotically sharp nonuniqueness result for the Zhikov problem on the torus
Tomasz Cieślak, Wojciech S. Ożański
We consider the stationary diffusion equation in -dimensional torus , where is a given forcing and is a…
Time-optimal control of a two-peakon collision
Tomasz Cieślak, Bidesh Das
We study a time-optimal control problem of a two-peakon collision. First, we state the controllability. Next, we find the time-optimal strategy. This is done via the HamiltonJacobi…
Geometric aspects of two- and threepeakons
Tomasz Cieślak, Wojciech Kryński
We apply geometric tools to study dynamics of two- and threepeakon solutions of the Camassa--Holm equation. New proofs of asymptotic behavior of the solutions are given. In particu…
Viscosity solutions to an initial value problem for a Hamilton--Jacobi equation with a degenerate Hamiltonian occurring in the dynamics of peakons
Tomasz Cieślak, Jakub Siemianowski, Andrzej Święch
We consider an initial value problem for a Hamilton--Jacobi equation with a quadratic and degenerate Hamiltonian. Our Hamiltonian comes from the dynamics of -peakon in the Camas…
Boundedness of solutions to the critical fully parabolic quasilinear one-dimensional Keller-Segel system
Bartosz Bieganowski, Tomasz Cieślak, Kentarou Fujie +1
In this paper we consider a one-dimensional fully parabolic quasilinear Keller-Segel system with critical nonlinear diffusion. We show uniform-in-time boundedness of solutions, whi…
Kinetic energy represented in terms of moments of vorticity and applications
Tomasz Cieślak, Krzysztof Oleszkiewicz, Marcin Preisner +1
We study 2d vortex sheets with unbounded support. First we show a version of the Biot- Savart law related to a class of objects including such vortex sheets. Next, we give a formul…