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Blow-up of a nonlocal $p$-Laplacian evolution equation with critical initial energy

Volume 117 / 2016

Yang Liu, Pengju Lv, Chaojiu Da Annales Polonici Mathematici 117 (2016), 89-99 MSC: Primary 35B44; Secondary 35K65. DOI: 10.4064/ap3807-1-2016 Published online: 23 May 2016

Abstract

This paper is concerned with the initial boundary value problem for a nonlocal $p$-Laplacian evolution equation with critical initial energy. In the framework of the energy method, we construct an unstable set and establish its invariance. Finally, the finite time blow-up of solutions is derived by a combination of the unstable set and the concavity method.

Authors

  • Yang LiuCollege of Mathematics and Computer Science
    Northwest University for Nationalities
    730124 Lanzhou, People’s Republic of China
    e-mail
  • Pengju LvDepartment of Medical Informatics
    Harbin Medical University
    163319 Daqing, People’s Republic of China
    e-mail
  • Chaojiu DaCollege of Mathematics and Computer Science
    Northwest University for Nationalities
    730124 Lanzhou, People’s Republic of China
    e-mail

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