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pro vyhledávání: '"Poláčik, Peter"'
Autor:
Pauthier, Antoine, Poláčik, Peter
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 $u_0=u(\cdot,0)$ have finite limits $\theta^\pm$ as $x\to\pm\infty$. We assume th
Externí odkaz:
http://arxiv.org/abs/2112.11160
Autor:
Poláčik, Peter, Valdebenito, Darío A.
We consider the equation $\Delta_x u+u_{yy}+f(u)=0,\ x=(x_1,\dots,x_N)\in\mathbb{R}^N,\ y\in \mathbb{R},$ where $N\geq 2$ and $f$ is a sufficiently smooth function satisfying $f(0)=0$, $f'(0)<0$, and some natural additional conditions. We prove that
Externí odkaz:
http://arxiv.org/abs/2008.08406
Autor:
Pauthier, Antoine, Poláčik, Peter
We continue our study of bounded solutions of the semilinear parabolic equation $u_t=u_{xx}+f(u)$ on the real line, where $f$ is a locally Lipschitz function on $\mathbb{R}.$ Assuming that the initial value $u_0=u(\cdot,0)$ of the solution has finite
Externí odkaz:
http://arxiv.org/abs/2001.10219
Autor:
Poláčik, Peter, Quittner, Pavol
We consider the semilinear heat equation $u_t=\Delta u+u^p$ on ${\mathbb R}^N$. Assuming that $N\ge 3$ and $p$ is greater than the Sobolev critical exponent $(N+2)/(N-2)$, we examine entire solutions (classical solutions defined for all $t\in {\mathb
Externí odkaz:
http://arxiv.org/abs/1907.07873
Autor:
Poláčik, Peter, Quittner, Pavol
In studies of superlinear parabolic equations \begin{equation*} u_t=\Delta u+u^p,\quad x\in {\mathbb R}^N,\ t>0, \end{equation*} where $p>1$, backward self-similar solutions play an important role. These are solutions of the form $ u(x,t) = (T-t)^{-1
Externí odkaz:
http://arxiv.org/abs/1906.11159
Autor:
Poláčik, Peter, Valdebenito, Darío A.
Publikováno v:
In Journal of Functional Analysis 15 June 2022 282(12)
Autor:
Pauthier, Antoine, Poláčik, Peter
We consider the semilinear parabolic equation $u_t=u_{xx}+f(u)$ on the real line, where $f$ is a locally Lipschitz function on $\mathbb{R}.$ We prove that if a solution $u$ of this equation is bounded and its initial value $u(x,0)$ has distinct limit
Externí odkaz:
http://arxiv.org/abs/1711.01499
Autor:
Pauthier, Antoine, Poláčik, Peter
Publikováno v:
In Journal de mathématiques pures et appliquées September 2021 153:137-186
Autor:
Földes, Juraj, Poláčik, Peter
We consider the Dirichlet problem u_t &= \Delta u + f(x, u, \nabla u)+ h(x, t),& \qquad &(x, t) \in \Omega \times (0, \infty), u &= 0, & \qquad &(x, t) \in \partial\Omega \times (0, \infty), on a bounded domain $\Omega \subset \mathbb{R}^N$. The doma
Externí odkaz:
http://arxiv.org/abs/1311.7050