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<p>We consider a time-fractional semilinear parabolic abstract Cauchy problem for a time-dependent sectorial operator <i>A</i>(<i>t</i>) which satisfies the Acquistapace–Terreni conditions. We first prove local existence results for the mild solution of the problem at hand. Then we prove, under suitable assumptions on the initial datum, that the solution is also global in time. This is achieved by proving ultracontractivity estimates for the fractional evolution families associated with the operator <i>A</i>(<i>t</i>).</p>

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Non-autonomous semilinear fractional evolution equations: well-posedness and ultracontractivity results

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月13日

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  • Simone Creo,
  • Maria Rosaria Lancia

摘要

We consider a time-fractional semilinear parabolic abstract Cauchy problem for a time-dependent sectorial operator A(t) which satisfies the Acquistapace–Terreni conditions. We first prove local existence results for the mild solution of the problem at hand. Then we prove, under suitable assumptions on the initial datum, that the solution is also global in time. This is achieved by proving ultracontractivity estimates for the fractional evolution families associated with the operator A(t).