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**Harvard**

Sabelnikov, V. och Lipatnikov, A. (2014) *Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection*.

** BibTeX **

@article{

Sabelnikov2014,

author={Sabelnikov, Vladimir and Lipatnikov, Andrei},

title={Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection},

journal={Physical Review E. Statistical, Nonlinear, and Soft Matter Physics},

issn={1539-3755},

volume={90},

issue={3},

pages={Art. no. 033004},

abstract={The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.},

year={2014},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 202786

A1 Sabelnikov, Vladimir

A1 Lipatnikov, Andrei

T1 Speed selection for traveling-wave solutions to the diffusion-reaction equation with cubic reaction term and Burgers nonlinear convection

YR 2014

JF Physical Review E. Statistical, Nonlinear, and Soft Matter Physics

SN 1539-3755

VO 90

IS 3

AB The problem of traveling wave (TW) speed selection for solutions to a generalized Murray-Burgers-KPP-Fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results. Depending on the magnitude of a parameter inherent in the reaction term (i) the term is either a concave function or a function with the inflection point and (ii) transition from pulled to pushed TW solution occurs due to interplay of two nonlinear terms; the reaction term and the Burgers convection term. Explicit pushed TW solutions are derived. It is shown that physically observable TW solutions, i.e., solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition, can be determined by seeking the TW solution characterized by the maximum decay rate at its leading edge. In the Appendix, the developed approach is applied to a non-linear diffusion-reaction equation that is widely used to model premixed turbulent combustion.

LA eng

DO 10.1103/PhysRevE.90.033004

LK https://journals.aps.org/pre/pdf/10.1103/PhysRevE.90.033004

LK http://publications.lib.chalmers.se/records/fulltext/202786/local_202786.pdf

OL 30