Relation between entire solutions and traveling wave solutions of the Allen-Cahn-Nagumo equation

Date(s) : 12/06/2018   iCal
11 h 00 min - 12 h 00 min

Propagation phenomena are often observed in many fields including dissipative situations. To characterize the universal profiles of these phenomena, traveling wave solutions and entire solutions play important roles. In this talk we focus on the Allen-Cahn-Nagumo equation, which is a single reaction diffusion equation with bistable nonlinearity. First we discuss the relation between traveling wave solutions and entire solutions among the known results. From the observation of their relation, I will introduce the zipping wave solutions and the entire solution whose level sets are approximately equidistant from any convex set as time goes to – infinity.


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