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Nguyen Anh Dao, Jesus Ildefonso Díaz; A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena; Journal of Mathematical Analysis and Applications, Vol. 437, pp. 445 – 473.


We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is considered in this paper.

Keywords: Degenerate parabolic equations; Gradient estimate; Quenching phenomenon; L1L1-initial datum; Free boundary