Singular solutions of parabolic $p$-Laplacian with absorption

• Autores: Xinfu Chen, Yuanwei Qi, Mingxin Wang
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 11, 2007, págs. 5653-5668
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04336-x
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• Resumen

  • 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 .