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arXiv · 0808.0783

Growth rate and extinction rate of a reaction diffusion equation with a singular nonlinearity

Kin Ming Hui
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Abstract

We prove the growth rate of global solutions of the equation $u_t=Δu-u^{-ν}$ in $\R^n\times (0,\infty)$, $u(x,0)=u_0>0$ in $\R^n$, where $ν>0$ is a constant. More precisely for any $0 1$. We also find various conditions on the initial value for the solution to extinct in a finite time and obtain the corresponding decay rate of the solution near the extinction time.

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Kin Ming Hui. 2008-08-06. Growth rate and extinction rate of a reaction diffusion equation with a singular nonlinearity. https://arxiv.org/abs/0808.0783

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