Asymptotic analysis of reaction-diffusion-advection problems: Fronts with periodic motion and blow-up

8th Workshop on Multi-Rate Processes and Hysteresis;HSFS Workshop (Hysteresis and Slow-Fast Systems)

Nefedov, Nikolay^1

Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow

119899, Russia^1

关键词: Asymptotic approximation;    Differential inequalities;    Existence and stability;    Initial-boundary value problems;    Parabolic problems;    Periodic solution;    Reaction diffusion;    Singularly perturbed;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/811/1/012008/pdf
DOI  :  10.1088/1742-6596/811/1/012008

来源: IOP

【 摘 要 】

This is an extended variant of the paper presented at MURPHYS-HSFS 2016 conference in Barcelona. We discuss further development of the asymptotic method of differential inequalities to investigate existence and stability of sharp internal layers (fronts) for nonlinear singularly perturbed periodic parabolic problems and initial boundary value problems with blow-up of fronts for reaction-diffusion-advection equations. In particular, we consider periodic solutions with internal layer in the case of balanced reaction. For the initial boundary value problems we prove the existence of fronts and give their asymptotic approximation including the new case of blowing-up fronts. This case we illustrate by the generalised Burgers equation.