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On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification |
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| Authors: | Nefedov N N Rudenko O V |
| Institution: | 1.Faculty of Physics, Moscow State University, Moscow, 119991, Russia ;2.Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, 119991, Russia ;3.Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, 123810, Russia ;4.Blekinge Institute of Technology, Karlskrona, Sweden ; |
| Abstract: | A singularly perturbed initial–boundary value problem for a parabolic equation known in applications as a Burgers-type or reaction–diffusion–advection equation is considered. An asymptotic approximation of solutions with a moving front is constructed in the case of modular and quadratic nonlinearity and nonlinear amplification. The influence exerted by nonlinear amplification on front propagation and blowing- up is determined. The front localization and the blowing-up time are estimated. |
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