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Global behaviour of solutions to some nonlinear diffusion equations. (English) Zbl 0719.35041
The authors study the problem $u_ t=\Delta u^ m+u^ p-au\text{ in } D\times (0,\infty)$ with given positive initial value $$u_ 0$$ and zero boundary values.
Among other things they prove a blow-up result for the case $$m=p$$, $$a>0$$. In the cases $$0<m<1$$, $$a=0$$ and $$0<m\leq p$$, $$a>0$$ they prove global existence and decay to zero (in the $$L^{\infty}$$ norm). If $$0<m<1$$ a “finite vanishing time” result is shown to hold.
Reviewer: R.Sperb (Zürich)
##### MSC:
 35K57 Reaction-diffusion equations 35B40 Asymptotic behavior of solutions to PDEs
##### Keywords:
blow-up; global existence; decay; finite vanishing time
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##### References:
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