P. Polácik

activity

20062021

most citedLarge-time behavior of solutions of parabolic equations on the real line with convergent initial data

8 citations · 8 across the 4 of their papers we have counts for

collaborators

5 papers

math.AP2021

Large-time behavior of solutions of parabolic equations on the real line with convergent initial data III:unstable limit at infinity

Antoine Pauthier, Peter Poláčik

This is a continuation, and conclusion, of our study of bounded solutions $u$ of the semilinear parabolic equation $u_{t} = u_{xx} + f (u)$ on the real line whose initial data $u_0=u(\cdo…

math.AP2020

The existence of partially localized periodic-quasiperiodic solutions and related KAM-type results for elliptic equations on the entire space

Peter Poláčik, Darío A. Valdebenito

We consider the equation $Δ_{x} u + u_{y y} + f (u) = 0, x = (x_{1}, \dots, x_{N}) \in R^{N}, y \in R,$ where $N \geq 2$ and $f$ is a sufficiently smooth function satisfying $f (0) = 0$ ,…

math.AP2017★ 8 cited

Large-time behavior of solutions of parabolic equations on the real line with convergent initial data

Antoine Pauthier, Peter Poláčik

We consider the semilinear parabolic equation $u_{t} = u_{xx} + f (u)$ on the real line, where $f$ is a locally Lipschitz function on $R .$ We prove that if a solution $u$ of this…

math.AP2012

Nonnegative solutions with a nontrivial nodal set for elliptic equations on smooth symmetric domains

Peter Polacik, Susanna Terracini

We consider a semilinear elliptic equation on a smooth bounded domain $\Om$ in $R^{2}$ , assuming that both the domain and the equation are invariant under reflections about one of t…

math.AP2006

Zeros of complex caloric functions and singularities of complex viscous Burgers equation

Peter Polacik, Vladimir Sverak

We show that the 1d viscous Burgers equation considered for complex valued functions develops finite-time singularities from compactly supported smooth data. By means of the Cole-H…