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<p>This work is devoted to the study of initial boundary value problem for <i>k</i>-component system of semilinear wave equations with several fundamental boundary conditions (namely, the Dirichlet, Neumann, and Robin boundary conditions). Blow-up results and lifespan estimates of solutions to the problem with two different types of weak damping terms and power nonlinearities in the sub-critical and critical cases on exterior domain are obtained. The test function technique is performed in the proofs. It is worth observing that our results in Theorem 1.1 in this article contain the results in [6] as a special case when <i>θ</i> = 0. To the best of our knowledge, the results in Theorems 1.1–1.2 are new.</p>

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Blow-up results for the weakly coupled system of semilinear wave equations with weak dampings

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Sen Ming,
  • Xiong-mei Fan,
  • Cui Ren,
  • Jin Xie

摘要

This work is devoted to the study of initial boundary value problem for k-component system of semilinear wave equations with several fundamental boundary conditions (namely, the Dirichlet, Neumann, and Robin boundary conditions). Blow-up results and lifespan estimates of solutions to the problem with two different types of weak damping terms and power nonlinearities in the sub-critical and critical cases on exterior domain are obtained. The test function technique is performed in the proofs. It is worth observing that our results in Theorem 1.1 in this article contain the results in [6] as a special case when θ = 0. To the best of our knowledge, the results in Theorems 1.1–1.2 are new.