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<p>We derive the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. The time-variable coefficient is recovered by solving the inverse abstract Cauchy problem using the solution operator representation. As a complement, we also study similar problems by considering almost sectorial operators that depend on a time-variable.</p>

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Direct and inverse abstract Cauchy problems with fractional powers of almost sectorial operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月11日

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  • Joel E. Restrepo

摘要

We derive the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. The time-variable coefficient is recovered by solving the inverse abstract Cauchy problem using the solution operator representation. As a complement, we also study similar problems by considering almost sectorial operators that depend on a time-variable.