Geodesic
Existence of a~solution in the form of a~moving front of a~reaction-diffusion-advection problem
Izvestiya. Mathematics , Tome 82 (2018) no. 5, pp. 984-1005

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We consider the initial-boundary value problem for an equation of reaction-diffusion-advection type in the case when the condition of balanced advection is satisfied. We give an algorithm for constructing an asymptotic representation of a solution which has the form of a moving front, obtain the equation of motion for the point of localization of the front, and prove the existence of that solution. The proof uses the asymptotic method of differential inequalities.
Keywords: small parameter, asymptotic methods, internal transition layer, differential inequalities.
Mots-clés : equation of reaction-diffusion-advection type, motion of a front 
@article{IM2_2018_82_5_a4,
     author = {N. T. Levashova and N. N. Nefedov and A. V. Yagremtsev},
     title = {Existence of a~solution in the form of a~moving front of a~reaction-diffusion-advection problem},
     journal = {Izvestiya. Mathematics },
     pages = {984--1005},
     publisher = {mathdoc},
     volume = {82},
     number = {5},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_5_a4/}
}
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N. T. Levashova; N. N. Nefedov; A. V. Yagremtsev. Existence of a~solution in the form of a~moving front of a~reaction-diffusion-advection problem. Izvestiya. Mathematics , Tome 82 (2018) no. 5, pp. 984-1005. http://geodesic.mathdoc.fr/item/IM2_2018_82_5_a4/