Non-Archimedean reaction-ultradiffusion equations and complex hierarchic systems

作者：Zuniga Galindo W A

来源：Nonlinearity, 2018, 31(6): 2590-2616.

DOI：10.1088/1361-6544/aab0b6

• energy landscapes
• free-energy functionals
• reaction-diffusion equations
• ultrametricity
• ultrametric spaces
• complex systems
• p-adic analysis

We initiate the study of non-Archimedean reaction-ultradiffusion equations and their connections with models of complex hierarchic systems. From a mathematical perspective, the equations studied here are the p-adic counterpart of the integro-differential models for phase separation introduced by Bates and Chmaj. Our equations are also generalizations of the ultradiffusion equations on trees studied in the 1980s by Ogielski, Stein, Bachas, Huberman, among others, and also generalizations of the master equations of the Avetisov et al models, which describe certain complex hierarchic systems. From a physical perspective, our equations are gradient flows of non-Archimedean free energy functionals and their solutions describe the macroscopic density profile of a bistable material whose space of states has an ultrametric structure. Some of our results are p-adic analogs of some well-known results in the Archimedean setting, however, the mechanism of diffusion is completely different due to the fact that it occurs in an ultrametric space.

• 出版日期2018-6