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- W2002160224 abstract "We study nonlinear diffusion problems of the form $u_t=u_{xx}+f(u)$ with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundaries representing the expanding fronts. For monostable, bistable, and combustion types of nonlinearities, Du and Lou [``Spreading and vanishing in nonlinear diffusion problems with free boundaries,” J. Eur. Math. Soc. (JEMS), to appear] obtained a rather complete description of the long-time dynamical behavior of the problem and revealed sharp transition phenomena between spreading ($lim_{ttoinfty}u(t,x)=1$) and vanishing ($lim_{ttoinfty}u(t,x)=0$). They also determined the asymptotic spreading speed of the fronts by making use of semiwaves when spreading happens. In this paper, we give a much sharper estimate for the spreading speed of the fronts than that in the above-mentioned work of Du and Lou, and we describe how the solution approaches the semiwave when spreading happens." @default.
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- W2002160224 date "2014-01-01" @default.
- W2002160224 modified "2023-09-30" @default.
- W2002160224 title "Sharp Estimate of the Spreading Speed Determined by Nonlinear Free Boundary Problems" @default.
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- W2002160224 doi "https://doi.org/10.1137/130908063" @default.
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