Zobrazeno 1 - 10
of 81
pro vyhledávání: '"Cieslak, Tomasz"'
Autor:
Bies, Piotr Michał, Cieślak, Tomasz
In the present paper, we study a model of a thermoelastic string that is initially heated. We classify all the possible asymptotic states when time tends to infinity of such a model. Actually, we show that whatever the initial data is, a heated strin
Externí odkaz:
http://arxiv.org/abs/2405.04310
The present note is devoted to the studies of the relation of the time-zero limits of Kaden's spirals and the 2D Euler equation. It is shown that the time-zero limits of Kaden's spirals satisfy inhomogeneous 2D Euler in a weak sense. As a corollary,
Externí odkaz:
http://arxiv.org/abs/2305.15356
We consider Alexander spirals with $M\geq 3$ branches, that is symmetric logarithmic spiral vortex sheets. We show that such vortex sheets are linearly unstable in the $L^\infty$ (Kelvin-Helmholtz) sense, as solutions to the Birkhoff-Rott equation. T
Externí odkaz:
http://arxiv.org/abs/2305.08764
Autor:
Bies, Piotr Michał, Cieślak, Tomasz
We construct unique regular solutions to the minimal nonlinear system of the 1d thermoelasticity. The obtained solution has a positive temperature. Our approach is based on an estimate, using the Fisher information, which seems completely new in this
Externí odkaz:
http://arxiv.org/abs/2303.12522
In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dimensional domain. Our main result establishes global-in-time existence o
Externí odkaz:
http://arxiv.org/abs/2303.09620
Here we study a nonlinear thermoelasticity hyperbolic-parabolic system describing the balance of momentum and internal energy of a heat-conducting elastic body, preserving the positivity of temperature. So far, no global existence results in such a n
Externí odkaz:
http://arxiv.org/abs/2210.09800
We consider a problem occurring in a magnetostatic levitation. The problem leads to a linear PDE in a strip. In engineering literature a particular solution is obtained. Such a solution enables one to compute lift and drag forces of the levitating ob
Externí odkaz:
http://arxiv.org/abs/2202.01570
Autor:
Cieślak, Tomasz, Ożański, Wojciech S.
Publikováno v:
Calc. Var. Partial Differ. Equ. 61, 97, 2022
We consider the stationary diffusion equation $-\mathrm{div} (\nabla u + bu )=f$ in $n$-dimensional torus $\mathbb{T}^n$, where $f\in H^{-1}$ is a given forcing and $b\in L^p$ is a divergence-free drift. Zhikov (Funkts. Anal. Prilozhen., 2004) consid
Externí odkaz:
http://arxiv.org/abs/2106.13674
Autor:
Cieślak, Tomasz, Das, Bidesh
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-Bellman equation and the dynamic programming method. We find a tricky
Externí odkaz:
http://arxiv.org/abs/2105.10343
Publikováno v:
In Journal of Differential Equations 25 April 2024 389:508-539
