Global Well Posedness for Damped Wave Models with Damping in the Memory

Authors

  • Hadj Kaddour Tayeb Faculty of Exact Sciences and Informatics, Mathematic Department, Hassiba Benbouali University, Chlef, Algeria
  • Ali Hakem Department of Technology, Laboratory ACEDP, Djilali Liabes University of Sidi Be- ` labbes, Algeria
  • Abdelkader Benali Faculty of Exact sciences and informatics, Mathematic Department, Hassiba Benbouali university, Chlef, Algeria
  • Ibrahim Alraddadi Ibrahim Alraddadi, Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia
  • Hijaz Ahmad Near East University, Operational Research Center in Healthcare, Near East Boulevard, PC: 99138 Nicosia/Mersin 10, Turkey
  • Taha Radwane Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
  • Dragan Pamucar Széchenyi István University, Győr, Hungary

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6266

Keywords:

damped wave equation, nonlinear memory, Cauchy problem, ; energy solutions, Matsumura type estimates, fixed point theorem

Abstract

This paper aims to study the Cauchy problem for damped wave models with a dissipative memory term. The main objective is to establish global (in time) well-posedness results for both energy solutions and higher-regularity solutions, determine the critical exponent in the Fujita sense, and investigate the influence of nonlinear memory on the Fujita exponent. Using modern tools from harmonic analysis and the Banach fixed point method, we show several results by taking into consideration different regularity properties of the initial data.

Author Biography

  • Hadj Kaddour Tayeb, Faculty of Exact Sciences and Informatics, Mathematic Department, Hassiba Benbouali University, Chlef, Algeria

    Laboratory of Mathematics and its Applications LMA, Hassiba Benbouali University
    of Chlef

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Partial Differential Equations and Dynamical Systems

License

Copyright (c) 2025 Hadj Kaddour Tayeb, Ali Hakem, Abdelkader Benali, Ibrahim Alraddadi, Hijaz Ahmad, Taha Radwane, Dragan Pamucar

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How to Cite

Global Well Posedness for Damped Wave Models with Damping in the Memory. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6266. https://doi.org/10.29020/nybg.ejpam.v18i4.6266