A Comparative Analysis of Methodologies for Oscillation Theory in
Parabolic Partial Differential Equations<o:p></o:p>

<span style="font-size: 16px; line-height: 107%; font-family: &quot;Times New Roman&quot;, serif;">Djamila Seba</span>

مجلة الجامعة الإسلامية للعلوم التطبيقية

A Comparative Analysis of Methodologies for Oscillation Theory in Parabolic Partial Differential Equations

Djamila Seba

الكلمات مفتاحية: Oscillation; Parabolic equation; Deviating arguments.

التخصص العام: Science

التخصص الدقيق: Differential equations

https://doi.org/10.63070/jesc.2025.028; Received 24 August 2025; Revised 21 September 2025; Accepted 05 October 2025; Available online 13 October 2025.
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الملخص

This paper presents a comprehensive review, from 1986 to 2001, of the literature concerning the oscillatory behavior of solutions to parabolic partial differential equations with deviating arguments. We focus on the development of criteria for oscillation, highlighting the effects of discrete and continuous distributed delays, nonlinearities, forcing terms, and various boundary conditions. The review synthesizes methodologies commonly employed in the field, such as the reduction to ordinary differential inequalities and the use of integral averaging techniques. Finally, we emphasize current trends and suggest potential directions for future research.

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