Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations

Peter Poláčik

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 301-310
  • ISSN: 0862-7959

Abstract

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We consider three types of semilinear second order PDEs on a cylindrical domain Ω × ( 0 , ∞ ) , where Ω is a bounded domain in ℝ N , N ≥ 2 . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of Ω × ( 0 , ∞ ) is reserved for time t , the third type is an elliptic equation with a singled out unbounded variable t . We discuss the asymptotic behavior, as t → ∞ , of solutions which are defined and bounded on Ω × ( 0 , ∞ ) .

How to cite

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Poláčik, Peter. "Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations." Mathematica Bohemica 127.2 (2002): 301-310. <http://eudml.org/doc/249038>.

@article{Poláčik2002,
abstract = {We consider three types of semilinear second order PDEs on a cylindrical domain $\Omega \times (0,\infty )$, where $\Omega $ is a bounded domain in $\{\{\mathbb \{R\}\}\}^N$, $N\ge 2$. Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of $\Omega \times (0,\infty )$ is reserved for time $t$, the third type is an elliptic equation with a singled out unbounded variable $t$. We discuss the asymptotic behavior, as $t\rightarrow \infty $, of solutions which are defined and bounded on $\Omega \times (0,\infty )$.},
author = {Poláčik, Peter},
journal = {Mathematica Bohemica},
keywords = {parabolic equations; elliptic equations; hyperbolic equations; asymptotic behavior; center manifold; cylindrical domain; center manifold},
language = {eng},
number = {2},
pages = {301-310},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations},
url = {http://eudml.org/doc/249038},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Poláčik, Peter
TI - Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 301
EP - 310
AB - We consider three types of semilinear second order PDEs on a cylindrical domain $\Omega \times (0,\infty )$, where $\Omega $ is a bounded domain in ${{\mathbb {R}}}^N$, $N\ge 2$. Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of $\Omega \times (0,\infty )$ is reserved for time $t$, the third type is an elliptic equation with a singled out unbounded variable $t$. We discuss the asymptotic behavior, as $t\rightarrow \infty $, of solutions which are defined and bounded on $\Omega \times (0,\infty )$.
LA - eng
KW - parabolic equations; elliptic equations; hyperbolic equations; asymptotic behavior; center manifold; cylindrical domain; center manifold
UR - http://eudml.org/doc/249038
ER -

References

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