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<p>In this paper, we demonstrate that the so-called expansion of positivity holds true for doubly nonlinear nonlocal parabolic type equations, having the fractional <i>p</i>-Laplace type operator and a power-nonlinearity in the time-derivative. The exponential time-stretching method originally developed for the local equations is transparently extended to the nonlocal equations in the scaling regime intrinsic to the doubly nonlinear nonlocal parabolic operator. The nonlocal effect of the nonlocal equations are given by the so-called tail.</p>

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Expansion of positivity for the doubly nonlinear parabolic fractional type equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月8日

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  • Masashi Misawa,
  • Yoshihiko Yamaura

摘要

In this paper, we demonstrate that the so-called expansion of positivity holds true for doubly nonlinear nonlocal parabolic type equations, having the fractional p-Laplace type operator and a power-nonlinearity in the time-derivative. The exponential time-stretching method originally developed for the local equations is transparently extended to the nonlocal equations in the scaling regime intrinsic to the doubly nonlinear nonlocal parabolic operator. The nonlocal effect of the nonlocal equations are given by the so-called tail.