Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Cauchy problem viscoelastic equation global existence blow up
• 年，卷（期）: 2018,（3）
• 页码范围: 224-236
• 页数: 13页
• 分类号: O175.27|O175.29
• 语种: 英文
• DOI: 10.4208/jpde.v31.n3.3

摘要

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.