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<p>In this paper, we investigate a coupled system of nonlinear wave equations involving Choi–MacCamy type fractional damping and fully coupled nonlinear source terms. We first establish the local well-posedness of solutions by using nonlinear semigroup theory. Then, we prove that solutions blow up in finite time under suitable conditions on the initial data, regardless of the sign of the initial energy. Explicit upper bounds for the lifespan of solutions are also derived. The main novelty of this work lies in the analysis of a strongly coupled system combining nonlocal fractional damping with nonlinear cross-interactions, which leads to significant analytical challenges due to the nonlocal memory effects. Finally, some numerical simulations are presented to illustrate the theoretical results.</p>

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Well-posedness and finite-time blow-up of a coupled wave system with fractional damping and nonlinear cross-interactions

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Radhouane Aounallah

摘要

In this paper, we investigate a coupled system of nonlinear wave equations involving Choi–MacCamy type fractional damping and fully coupled nonlinear source terms. We first establish the local well-posedness of solutions by using nonlinear semigroup theory. Then, we prove that solutions blow up in finite time under suitable conditions on the initial data, regardless of the sign of the initial energy. Explicit upper bounds for the lifespan of solutions are also derived. The main novelty of this work lies in the analysis of a strongly coupled system combining nonlocal fractional damping with nonlinear cross-interactions, which leads to significant analytical challenges due to the nonlocal memory effects. Finally, some numerical simulations are presented to illustrate the theoretical results.