Geodesic
On the motion, amplification, and blow-up of fronts in Burgers-type equations with quadratic and modular nonlinearity
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 26-31 Cet article a éte moissonné depuis la source Math-Net.Ru

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A singularly perturbed initial-boundary value problem for a parabolic equation, which is called in applications an equation of Burgers type, is considered. Existence conditions are obtained, and an asymptotic approximation of a new class of solutions with a moving front is constructed. The results are applied to problems with quadratic and modular nonlinearity and nonlinear amplification. The influence of nonlinear amplification on the propagation and destruction of fronts is revealed. Estimates for the blow-up localization and blow-up time are obtained.
Keywords: singularly perturbed parabolic problems, equations of Burgers type, internal layers, asymptotic, methods, blow-up of solutions.
Mots-clés : reaction–diffusion–advection equations, fronts 
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     author = {N. N. Nefedov and O. V. Rudenko},
     title = {On the motion, amplification, and blow-up of fronts in {Burgers-type} equations with quadratic and modular nonlinearity},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
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N. N. Nefedov; O. V. Rudenko. On the motion, amplification, and blow-up of fronts in Burgers-type equations with quadratic and modular nonlinearity. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 493 (2020), pp. 26-31. http://geodesic.mathdoc.fr/item/DANMA_2020_493_a5/

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