Geodesic
Extinction for fast diffusion equations with nonlinear sources
Electronic journal of differential equations, Tome 2005 (2005)
We establish conditions for the extinction of solutions, in finite time, of the fast diffusion problem $u_t=\Delta u^m+\lambda u^p, 0 less than m less than 1$, in a bounded domain of $R^N$ with $N greater than 2$. More precisely, we show that if $p greater than m$, the solution with small initial data vanishes in finite time, and if $p less than m$, the maximal solution is positive for all $t greater than 0$. If $p=m$, then first eigenvalue of the Dirichlet problem plays a role.
Classification : 35K20, 35K55
Keywords: extinction, fast diffusion, first eigenvalue 
@article{EJDE_2005__2005__a190,
     author = {Li,  Yuxiang and Wu,  Jichun},
     title = {Extinction for fast diffusion equations with nonlinear sources},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1073.35134},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a190/}
}
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AU  - Wu,  Jichun
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JO  - Electronic journal of differential equations
PY  - 2005
VL  - 2005
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%0 Journal Article
%A Li,  Yuxiang
%A Wu,  Jichun
%T Extinction for fast diffusion equations with nonlinear sources
%J Electronic journal of differential equations
%D 2005
%V 2005
%U http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a190/
%G en
%F EJDE_2005__2005__a190
Li,  Yuxiang; Wu,  Jichun. Extinction for fast diffusion equations with nonlinear sources. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a190/