Abstract
This paper treats some non-linear diffusion system arising from the population growth as well as the classical diffusion and heat conduction problem. The spatial domain in the diffusion system can be either bounded or unbounded and the boundary condition under consideration includes both Dirichlet and Neumann type conditions. It is shown under some physically reasonable conditions on the non-linear function that the initial boundary value problem has a unique bounded positive solution which can be constructed by the method of successive approximation. In some simple models, a recursion formula for the calculation of the approximation is given. In addition to the existence problem the investigation is devoted to the asymptotic behavior of the solution and the stability of a steady-state solution. Particular attention is given to a model in the population growth and the chemical diffusion system.
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