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Reaction-diffusion equations with degenerate nonlinear diffusion are in widespread use as
models of biological phenomena. This paper begins with a survey of applications to
ecology, cell biology and bacterial colony patterns. The author then reviews mathematical
results on the existence of travelling wave front solutions of these equations, and their
generation from given initial data. A detailed study is then presented of the form of
smooth-front...
In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data . The analytic initial data can be extended as holomorphic functions in a strip around the -axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).
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