科研之友
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摘要
We study a nonlinear diffusion equation u(t) + f(u) with Robin boundary condition at x = 0 and with a free boundary condition at x = h(t), where h(t) > 0 is a moving boundary representing the expanding front in ecology models. For any f is an element of C-1 with f(0) = 0, we prove that every bounded positive solution of this problem converges to a stationary one. As applications, we use this convergence result to study diffusion equations with rnonostable and combustion types of nonlinearities. We obtain dichotomy results and sharp thresholds for the asymptotic behavior of the solutions.
- 出版日期2013
- 单位同济大学
