Resumen de Singular solutions of parabolic $p$-Laplacian with absorption

Xinfu Chen, Yuanwei Qi, Mingxin Wang

• We consider, for and , the -Laplacian evolution equation with absorption We are interested in those solutions, which we call singular solutions, that are non-negative, non-trivial, continuous in , and satisfy for all . We prove the following:

  (i) When , there does not exist any such singular solution.

  (ii) When , there exists, for every , a unique singular solution that satisfies as .

  Also, as , where is a singular solution that satisfies as .

  Furthermore, any singular solution is either or for some finite positive .