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<p>In this paper, we study the initial-boundary value problem for a model equation of higher-order Kirchhoff-type in a bounded domain. The existence of local and global solutions for this problem are proved by means of the contraction mapping criterion and potential well method. Meanwhile, we obtain the blow-up result of solution in the unstable set by using the concavity analysis method and give the lifespan estimate of solution.</p>

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Existence and blow-up of solutions for higher-order Kirchhoff-type equation

  • 期刊论文

  • 发表日期：

    2025年2月20日

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  • Yaojun Ye,
  • Shuting Chang

摘要

In this paper, we study the initial-boundary value problem for a model equation of higher-order Kirchhoff-type in a bounded domain. The existence of local and global solutions for this problem are proved by means of the contraction mapping criterion and potential well method. Meanwhile, we obtain the blow-up result of solution in the unstable set by using the concavity analysis method and give the lifespan estimate of solution.