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

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

2008-08-06

arxiv.org/abs/0808.0783v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

We prove the growth rate of global solutions of the equation $u_t=\Delta u-u^{-\nu}$ in $\R^n\times (0,\infty)$, $u(x,0)=u_0>0$ in $\R^n$, where $\nu>0$ is a constant. More precisely for any $01$. 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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