Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium

• Autorzy: Milena Dimova , Stefka Dimova , Daniela Vasileva
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Nonlinear elliptic and parabolic problems; Self-similar solutions; Blow-up; Structural stability; Metastability; Numerical methods

Kategorie tematyczne

• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 35B44: Blow-up
• 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 65P40: Nonlinear stabilities

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 8
• Strony: 1375-1391

Daty

wydano

2013-08-01

online

2013-05-22

Twórcy

autor

Milena Dimova

• Bulgarian Academy of Sciences

autor

Stefka Dimova

• Sofia University “St. Kl. Ohridski”

autor

Daniela Vasileva

• Bulgarian Academy of Sciences

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0253-5