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Finite extinction time for nonlinear parabolic equations with nonlinear mixed boundary data. (English) Zbl 0910.35069
The finite extinction phenomenon for nonlinear diffusion equations has drawn the interests of many authors. Using comparison arguments the authors study necessary and sufficient conditions on $\varphi$, $f$ and $g$ for a (weak) solution of $$u_t= \Delta \varphi (u)\pm f(x,t,u) \quad \text{in } \Omega \times (0,T),$$ with ${\partial \over \partial n} \varphi (u)= \mp g(x,t,u)$ on $\partial\Omega \times(0,T)$ and $u(x,0)= u_0(x)\ge 0$, either to have a finite extinction time or to stay positive for all $t\in (0,T)$. Special attention is given to the balance between the source $(+)$ and the absorption $(-)$ term.

##### MSC:
 35K60 Nonlinear initial value problems for linear parabolic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
##### Keywords:
source term; absorbtion term
Full Text:
##### References:
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