In this paper, the authors investigate a class of fast-diffusion p-Laplace equation, which was considered by Li, Han and Li (2016) [1], where, among other things, blow-up in finite time of solutions was proved for positive but suitably small initial energy. Their results will be complemented in this paper in the sense that the existence of finite time blow-up solutions for arbitrarily high initial energy will be proved. Moreover, an abstract criterion for the existence of global solutions that vanish at infinity will also be provided for high initial energy.

Accepted:

Published online:

*p*-Laplace, High initial energy, Global existence, Blow up

Yuzhu Han ^{1}

@article{CRMECA_2018__346_12_1153_0, author = {Yuzhu Han}, title = {A class of fast diffusion {\protect\emph{p}-Laplace} equation with arbitrarily high initial energy}, journal = {Comptes Rendus. M\'ecanique}, pages = {1153--1158}, publisher = {Elsevier}, volume = {346}, number = {12}, year = {2018}, doi = {10.1016/j.crme.2018.06.013}, language = {en}, }

Yuzhu Han. A class of fast diffusionp-Laplace equation with arbitrarily high initial energy. Comptes Rendus. Mécanique, Volume 346 (2018) no. 12, pp. 1153-1158. doi : 10.1016/j.crme.2018.06.013. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.06.013/

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^{☆} The author is supported by NSFC (11401252) and by Science and Technology Development Project of Jilin Province (20160520103JH).

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