Abstract
We consider positive solutions of the initial value problem foru t=Δu+u p in conesD=R +×Ω⊆R N (Ω⊆S N−1). In an earlier paper, we determined a critical exponentp *(Ω) with the following properties: (a) if 1<p<p *, then all nontrivial solutions blow up in finite time (blowup case); (b) ifp>p *, then there are nontrivial global solutions (global existence case). Here we show thatp * belongs to the blowup case. This generalizes a well-known result for the critical exponentp *=1+2/N inD=R N.
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Levine, H.A., Meier, P. A blowup result for the critical exponent in cones. Israel J. Math. 67, 129–136 (1989). https://doi.org/10.1007/BF02937290
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DOI: https://doi.org/10.1007/BF02937290