This article is cited in 1 paper

The existence and non-existence of traveling waves of scalar reaction-diffusion-advection equation in unbounded cylinder

Meng Haixia

School of Mathematics, Physics and Software Engineering, Lanzhou Jiaoton University Lanzhou, Gansu 730070, People’s Republic of China

Abstract: This paper is concerned with the existence and non-existence of traveling wave solutions of reaction-diffusion-advection equation with boundary conditions of mixed type in unbounded cylinder. By constructing new supper-sub solutions and applying monotone iteration method, we obtain existence of traveling wave solutions with wave velocity bigger than the “minimal speed”. For wave velocity smaller than the “minimal speed”, we find that traveling waves of exponential decay do not exist. Finally, we apply our results to KPP type nonlinearity.

Key words: traveling waves, existence, non-existence, boundary conditions of mixed type, wave speed.

UDC: 519.634

Received: 10.10.2012

Language: English

DOI: 10.7868/S0044466913110069

 English version: Computational Mathematics and Mathematical Physics, 2013, 53:11, 1644–1652

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