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On quasilinear parabolic equations involving measure data. (English) Zbl 0733.35017

The equation \(u_ t-div(| \nabla u|^{p-2}\nabla u)+u^ q=0\) with \(p>2,q>0\) is considered. Here \(x\in {\mathbb{R}}^ N\), \(0<t<T\) and \(u(x,0)=0\) for \(x\neq 0\). Generalizing known results for \(p=2\) and for the porous media equation, a positive singularity at \(x=0\), \(t=0\) is shown to be removable if and only if \(q>p-1+p/N\).

MSC:

35B60 Continuation and prolongation of solutions to PDEs
35K65 Degenerate parabolic equations
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