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<p>We study linear abstract differential-algebraic equations (ADAEs), and we introduce an index concept which is based on polynomial growth of a&#xa0;pseudo-resolvent. Our approach to solvability analysis is based on degenerate semigroups. We apply our results to some examples such as distributed circuit elements and a system obtained by heat-wave coupling.</p>

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A pseudo-resolvent approach to abstract differential-algebraic equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月6日

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  • Hannes Gernandt,
  • Timo Reis

摘要

We study linear abstract differential-algebraic equations (ADAEs), and we introduce an index concept which is based on polynomial growth of a pseudo-resolvent. Our approach to solvability analysis is based on degenerate semigroups. We apply our results to some examples such as distributed circuit elements and a system obtained by heat-wave coupling.