Global Existence for Population Evacuation Model

with Adaptability

Abstract

In the evacuation of the population, how to evacuate(diffusion) population more effectively is a very important question. Adaptive is defined as follows: population move(migration) toward the place where resource is intensive. The evacuation here not only refers to evacuation of population, also can say the diffusion of species evolution. Research on these problems is widely used in biology, sociology.

In this paper we consider two identical population that take different strategies in the same environment—one taking a random free diffusion strategy, another taking diffusion strategy with adaptability –competition evolution model, and prove that the time interval of the classical solution existence uniqueness.

Key words: diffusion, partial differential equations, adaptability, existence of global solution

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