108 citations · 111 across the 3 of their papers we have counts for
7 papers
Existence of viscosity solutions with the optimal regularity of a two-peakon Hamilton--Jacobi equation
Tomasz Cieślak, Jakub Siemianowski
This work is devoted to the studies of a Hamilton--Jacobi equation with a quadratic and degenerate Hamiltonian, which comes from the dynamics of a multipeakon in the Camassa--Holm…
A model in one-dimensional thermoelasticity
Tomasz Cieslak, Marija Galić, Boris Muha
We study a one-dimensional nonlinear hyperbolic-parabolic initial boundary value problem occurring in the theory of thermoelasticity. We prove existence and uniqueness of the local…
Maximal dissipation in Hunter-Saxton equation for bounded energy initial data
Tomasz Cieślak, Grzegorz Jamróz
In [Zhang and Zheng, 2005] it was conjectured by Zhang and Zheng that dissipative solutions of the Hunter-Saxton equation, which are known to be unique in the class of weak solutio…
A theorem on measures in dimension 2 and applications to vortex sheets
Tomasz Cieslak, Marta Szumanska
We find conditions under which measures belong to . Next we show that measures generated by Prandtl, Kaden as well as Pullin spirals, objects considered by physicists as incompress…
Long-time behavior of an angiogenesis model with flux at the tumor boundary
Tomasz Cieslak, Cristian Morales-Rodrigo
This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor ang…
Finite-time blowup in a supercritical quasilinear parabolic-parabolic Keller-Segel system in dimension 2
Tomasz Cieślak, Christian Stinner
In this paper we prove finite-time blowup of radially symmetric solutions to the quasilinear parabolic-parabolic two-dimensional Keller-Segel system for any positive mass. This is…
Global existence vs. blowup for the one dimensional quasilinear Smoluchowski-Poisson system
Tomasz Cieslak, Philippe Laurencot
We prove that, unlike in several space dimensions, there is no critical (nonlinear) diffusion coefficient for which solutions to the one dimensional quasilinear Smoluchowski-Poisso…