Volume 31, Issue 3
Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem

Gongwei Liu and Shuying Tian

10.4208/jpde.v31.n3.3

J. Part. Diff. Eq., 31 (2018), pp. 224-236.

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  • Abstract

The Cauchy problem for a viscoelastic equation with nonlinear damping and source terms is considered. We establish the nonexistence result of global solutions with initial energy controlled above by a critical value by modifying the method introduced in a work by Autuori et al. in 2010. Then we establish global existence for arbitrary initial data or the energy in potential well. These improve earlier results in the literatures.

  • History

Published online: 2018-09

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