88 citations · 658 across the 31 of their papers we have counts for
9 papers · 1 filter
Equivariant wave maps exterior to a ball
Piotr Bizoń, Tadeusz Chmaj, Maciej Maliborski
We consider the exterior Cauchy-Dirichlet problem for equivariant wave maps from 3+1 dimensional Minkowski spacetime into the three-sphere. Using mixed analytical and numerical met…
Dynamics near the threshold for blowup in the one-dimensional focusing nonlinear Klein-Gordon equation
Piotr Bizoń, Tadeusz Chmaj, Nikodem Szpak
We study dynamics near the threshold for blowup in the focusing nonlinear Klein-Gordon equation on the line. Using mixed numerical and analytica…
A note on late-time tails of spherical nonlinear waves
Piotr Bizoń, Tadeusz Chmaj, Andrzej Rostworowski
We consider the long-time behavior of small amplitude solutions of the semilinear wave equation in odd spatial dimensions. We show that for the quadratic non…
Huygens' principle and anomalously small radiation tails
Piotr Bizoń
This is a short account of recent joint work with T. Chmaj and A. Rostworowski on asymptotic behavior of linear and nonlinear waves, as presented at the conference devoted to Myron…
Linear and nonlinear tails II: exact decay rates in spherical symmetry
Nikodem Szpak, Piotr Bizoń, Tadeusz Chmaj +1
We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the comp…
On asymptotic stability of the Skyrmion
Piotr Bizoń, Tadeusz Chmaj, Andrzej Rostworowski
We study the asymptotic behavior of spherically symmetric solutions in the Skyrme model. We show that the relaxation to the degree-one soliton (called the Skyrmion) has a universal…
On convergence towards a self-similar solution for a nonlinear wave equation - a case study
Piotr Bizoń, Tadeusz Chmaj
We consider the problem of asymptotic stability of a self-similar attractor for a simple semilinear radial wave equation which arises in the study of the Yang-Mills equations in 5+…
On blowup for semilinear wave equations with a focusing nonlinearity
Piotr Bizoń, Tadeusz Chmaj, Zbislaw Tabor
In this paper we report on numerical studies of formation of singularities for the semilinear wave equations with a focusing power nonlinearity in three space…
Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere
Piotr Bizoń, Tadeusz Chmaj, Zbislaw Tabor
In this paper we report on numerical studies of the Cauchy problem for equivariant wave maps from 2+1 dimensional Minkowski spacetime into the two-sphere. Our results provide stron…