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The conditions for blow-up and global existence of solution for a degenerate and singular parabolic equation with a non-local source. (English) Zbl 1479.35149

Summary: In this paper, we consider the degenerate and singular porous medium equation with a non-local source \(v_\tau=\left(\xi^\beta(v^m)_\xi\right)_\xi+\int_0^aF(v^m)d\xi\) The conditions on the local and global existence of solutions are investigated. In the case of blow-up, the blow-up set is shown. Moreover, the uniform blow-up profile of the blow-up solution is given.

MSC:

35B44 Blow-up in context of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35K67 Singular parabolic equations
35K65 Degenerate parabolic equations
35R09 Integro-partial differential equations
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