Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium
Milena Dimova; Stefka Dimova; Daniela Vasileva
Open Mathematics (2013)
- Volume: 11, Issue: 8, page 1375-1391
- ISSN: 2391-5455
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topMilena Dimova, Stefka Dimova, and Daniela Vasileva. "Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium." Open Mathematics 11.8 (2013): 1375-1391. <http://eudml.org/doc/269508>.
@article{MilenaDimova2013,
abstract = {The paper contributes to the problem of finding all possible structures and waves, which may arise and preserve themselves in the open nonlinear medium, described by the mathematical model of heat structures. A new class of self-similar blow-up solutions of this model is constructed numerically and their stability is investigated. An effective and reliable numerical approach is developed and implemented for solving the nonlinear elliptic self-similar problem and the parabolic problem. This approach is consistent with the peculiarities of the problems - multiple solutions of the elliptic problem and blow-up solutions of the parabolic one.},
author = {Milena Dimova, Stefka Dimova, Daniela Vasileva},
journal = {Open Mathematics},
keywords = {Nonlinear elliptic and parabolic problems; Self-similar solutions; Blow-up; Structural stability; Metastability; Numerical methods; nonlinear parabolic problems; self-similar solutions; blow-up; structural stability; metastability; numerical examples; nonlinear elliptic self-similar problem},
language = {eng},
number = {8},
pages = {1375-1391},
title = {Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium},
url = {http://eudml.org/doc/269508},
volume = {11},
year = {2013},
}
TY - JOUR
AU - Milena Dimova
AU - Stefka Dimova
AU - Daniela Vasileva
TI - Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium
JO - Open Mathematics
PY - 2013
VL - 11
IS - 8
SP - 1375
EP - 1391
AB - The paper contributes to the problem of finding all possible structures and waves, which may arise and preserve themselves in the open nonlinear medium, described by the mathematical model of heat structures. A new class of self-similar blow-up solutions of this model is constructed numerically and their stability is investigated. An effective and reliable numerical approach is developed and implemented for solving the nonlinear elliptic self-similar problem and the parabolic problem. This approach is consistent with the peculiarities of the problems - multiple solutions of the elliptic problem and blow-up solutions of the parabolic one.
LA - eng
KW - Nonlinear elliptic and parabolic problems; Self-similar solutions; Blow-up; Structural stability; Metastability; Numerical methods; nonlinear parabolic problems; self-similar solutions; blow-up; structural stability; metastability; numerical examples; nonlinear elliptic self-similar problem
UR - http://eudml.org/doc/269508
ER -
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