Geodesic
Asymptotic Behavior of Solutions to Diffusion Problems with Robin and Free Boundary Conditions
X. Liu1 ; B. Lou1
1 Department of Mathematics, Tongji University, Shanghai 200092, China
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 3, pp. 18-32 Cet article a éte moissonné depuis la source EDP Sciences

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We study a nonlinear diffusion equation ut = uxx + 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 ∈ C1 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 monostable and combustion types of nonlinearities. We obtain dichotomy results and sharp thresholds for the asymptotic behavior of the solutions.
DOI : 10.1051/mmnp/20138303

X. Liu 1 ; B. Lou 1

1 Department of Mathematics, Tongji University, Shanghai 200092, China 
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X. Liu; B. Lou. Asymptotic Behavior of Solutions to Diffusion Problems with Robin and Free Boundary Conditions. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 3, pp. 18-32. doi: 10.1051/mmnp/20138303

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