On movable singularities of self-similar solutions of semilinear wave equations

Radosław A. Kycia

Banach Center Publications (2012)

  • Volume: 97, Issue: 1, page 59-72
  • ISSN: 0137-6934

Abstract

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In this paper we analyze movable singularities of the solutions of the equation for self-similar profiles resulting from semilinear wave equation. We study local analytic solutions around two fixed singularity points of this equation- ρ = 0 and ρ = 1. The movable singularities of local analytic solutions at the origin will be connected with those of the Lane-Emden equation. The function describing approximately their position on the complex plane will be derived. For ρ > 1 some topological considerations will be presented that describe movable singularity of local analytic solution at ρ = 1. Numerical illustrations of the results will also be provided.

How to cite

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Radosław A. Kycia. "On movable singularities of self-similar solutions of semilinear wave equations." Banach Center Publications 97.1 (2012): 59-72. <http://eudml.org/doc/281857>.

@article{RadosławA2012,
abstract = {In this paper we analyze movable singularities of the solutions of the equation for self-similar profiles resulting from semilinear wave equation. We study local analytic solutions around two fixed singularity points of this equation- ρ = 0 and ρ = 1. The movable singularities of local analytic solutions at the origin will be connected with those of the Lane-Emden equation. The function describing approximately their position on the complex plane will be derived. For ρ > 1 some topological considerations will be presented that describe movable singularity of local analytic solution at ρ = 1. Numerical illustrations of the results will also be provided.},
author = {Radosław A. Kycia},
journal = {Banach Center Publications},
keywords = {movable singularity; semilinear wave equation; self-similar profiles},
language = {eng},
number = {1},
pages = {59-72},
title = {On movable singularities of self-similar solutions of semilinear wave equations},
url = {http://eudml.org/doc/281857},
volume = {97},
year = {2012},
}

TY - JOUR
AU - Radosław A. Kycia
TI - On movable singularities of self-similar solutions of semilinear wave equations
JO - Banach Center Publications
PY - 2012
VL - 97
IS - 1
SP - 59
EP - 72
AB - In this paper we analyze movable singularities of the solutions of the equation for self-similar profiles resulting from semilinear wave equation. We study local analytic solutions around two fixed singularity points of this equation- ρ = 0 and ρ = 1. The movable singularities of local analytic solutions at the origin will be connected with those of the Lane-Emden equation. The function describing approximately their position on the complex plane will be derived. For ρ > 1 some topological considerations will be presented that describe movable singularity of local analytic solution at ρ = 1. Numerical illustrations of the results will also be provided.
LA - eng
KW - movable singularity; semilinear wave equation; self-similar profiles
UR - http://eudml.org/doc/281857
ER -

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