Zobrazeno 1 - 10 of 92 pro vyhledávání: '"Peter Poláčik"'
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Large-time behavior of solutions of parabolic equations on the real line with convergent initial data II: Equal limits at infinity
Autor: Peter Poláčik, Antoine Pauthier
Publikováno v: Journal de Mathématiques Pures et Appliquées. 153:137-186
We continue our study of bounded solutions of the semilinear parabolic equation u t = u x x + f ( u ) on the real line, where f is a locally Lipschitz function on R . Assuming that the initial value u 0 = u ( ⋅ , 0 ) of the solution has finite limi
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3a905ca4c3bcdbc13f4a60ed8ca8ece8
https://doi.org/10.1016/j.matpur.2021.07.002
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3
The Existence of Partially Localized Periodic–Quasiperiodic Solutions and Related KAM-Type Results for Elliptic Equations on the Entire Space
Autor: Peter Poláčik, Darío A. Valdebenito
Publikováno v: Journal of Dynamics and Differential Equations. 34:3035-3056
We consider the equation 1 $$\begin{aligned} \Delta _x u+u_{yy}+f(u)=0,\quad x=(x_1,\dots ,x_N)\in {{\mathbb {R}}}^N,\ y\in {{\mathbb {R}}}, \end{aligned}$$ where $$N\ge 2$$ and f is a sufficiently smooth function satisfying $$f(0)=0$$ , $$f'(0)
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::01dac787105b6dfb70c078838212b5d8
https://doi.org/10.1007/s10884-020-09925-5
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5
Entire solutions and a Liouville theorem for a class of parabolic equations on the real line
Autor: Peter Poláčik
Publikováno v: Proceedings of the American Mathematical Society. 148:2997-3008
We consider a class of semilinear heat equations on R \mathbb {R} , including in particular the Fujita equation u t = u x x + | u | p − 1 u , x ∈ R , t ∈ R , \begin{equation*} u_t=u_{xx} +|u|^{p-1}u,\quad x\in \mathbb {R},\ t\in \mathbb {R}, \e
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::fb3d9e7359d26c154adee681ceaedd68
https://doi.org/10.1090/proc/14978
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6
Existence of quasiperiodic solutions of elliptic equations on the entire space with a quadratic nonlinearity
Autor: Peter Poláčik, Darío A. Valdebenito
Publikováno v: Discrete & Continuous Dynamical Systems - S. 13:1369-1393
We consider the equation \begin{document}$\Delta u+{{u}_{yy}}+f(x,u) = 0,\quad (x,y)\in {{\mathbb{R}}^{N}}\times \mathbb{R}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left( 1 \right)$ \end{document} where \begin{document}$ f $\end{document} is s
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::38f6d678048a85f95e737f3b3b5f8700
https://doi.org/10.3934/dcdss.2020077
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7
Dynamics of nonnegative solutions of one-dimensional reaction-diffusion equations with localized initial data. Part II: Generic nonlinearities
Autor: Peter Poláčik, Hiroshi Matano
Publikováno v: Communications in Partial Differential Equations. 45:483-524
We consider the Cauchy problem ut=uxx+f(u), x∈R,t>0,u(x,0)=u0(x), x∈R, where f is a C1 function on R with f(0)=0, and u0 is a nonnegative continuous function on R whose limits at ±∞ are equal to 0....
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::eb67e4fc4c66ecb789dc11790a63025b
https://doi.org/10.1080/03605302.2019.1700273
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8
Some generic properties of Schrödinger operators with radial potentials
Autor: Peter Poláčik, Darío A. Valdebenito
Publikováno v: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 149:1435-1451
We consider a class of Schrödinger operators on ${\open R}^N$ with radial potentials. Viewing them as self-adjoint operators on the space of radially symmetric functions in $L^2({\open R}^N)$, we show that the following properties are generic with r
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b9ff47671fd2f665f720d5151bfd048d
https://doi.org/10.1017/prm.2018.129
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