Analysis On A Reaction-diffusion Model For Two-language Competition

Language is an important medium of communication and it is the main way for people to communicate.With the development of a society and the migration of population,contact and interaction between different languages appear inevitably,then language competition occur.Language competition refers to the contradiction caused by different languages which used in communication.Language competition reflects people's attitude towards different languages,which in turn affects people's choice and use of languages.The author hypothesized that the self-growth of the two groups of people evolved according to the Logistic equations in [5].While in this paper,we assume that the self-growth of the two groups of people evolved according to a linear equation(refer to [39] and it's literature).We consider two kinds of boundary conditions : constant Dirichlet boundary value condition and homogeneous Neumann boundary value condition.By using eigenvalue method and Lyapunov method,we proved the linear stability and non-linear stability of the equilibrium solution.Our results show that when population increases linearly,weak and strong languages are more likely to coexist than the conclusions in [5].