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<p>We study the blow-up property of solution for a transport equation with nonlocal velocity and time-dependent nonlinear damping. Under certain conditions, we show that if the initial data is positive at some point, the smooth solution blows up in finite time.</p>

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The Blow-up of Solutions to a Transport Equation with Nonlocal Velocity and Time-dependent Nonlinear Damping

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • You Li,
  • Yan-nan Liu,
  • Ting-yu Xu

摘要

We study the blow-up property of solution for a transport equation with nonlocal velocity and time-dependent nonlinear damping. Under certain conditions, we show that if the initial data is positive at some point, the smooth solution blows up in finite time.