# 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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