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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
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References:
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