Stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity |
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Authors: | Zhaoxing Yang Guobao Zhang |
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Institution: | 1.College of Mathematics and Statistics,Northwest Normal University,Lanzhou,China |
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Abstract: | This paper is concerned with the stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity. By using the anti-weighted energy method and nonlin-ear Halanay’s inequality, we prove that all noncritical traveling waves (waves with speeds c > c*, c* is minimal speed) are time-exponentially stable, when the initial perturbations around the waves are small. As a corollary of our stability result, we immediately obtain the uniqueness of the traveling waves. |
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