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<p>This paper presents a comprehensive survey of the relaxed-type equations, a class of partial differential equations that extend the Fourier and Fickian-type equations by incorporating the finite propagation speed concept or micro-structural interactions influences. It explores the theoretical foundations of such equations, examines their mathematical properties, and highlights their significance in modeling different physical phenomena in a variety of applications. Moreover, recent advances and future prospects from various scientific fields are provided, opening the door for further research in this dynamic and developing field of study.</p>

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A survey on relaxed-type equations with applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月4日

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  • M. Khalaf,
  • Eman F. El‐Gazar

摘要

This paper presents a comprehensive survey of the relaxed-type equations, a class of partial differential equations that extend the Fourier and Fickian-type equations by incorporating the finite propagation speed concept or micro-structural interactions influences. It explores the theoretical foundations of such equations, examines their mathematical properties, and highlights their significance in modeling different physical phenomena in a variety of applications. Moreover, recent advances and future prospects from various scientific fields are provided, opening the door for further research in this dynamic and developing field of study.