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Local existence and blow up for the wave equation with nonlinear logarithmic source term and nonlinear dynamical boundary conditions combined with distributed delay

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Abstract

In this paper we highlight a type of hyperbolic equation relating the logarithmic source term with distributed delay and dynamic boundary condition. We get, under comfortable primary data is the weak solution to local existence. The results of the solutions were found using the Faydo–Galerkin method and Schoder’s fixed point theorem. Then, the minimum blow-up result was studied. Our work is an extension of some previous work.

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Authors and Affiliations

  1. Department of Material Sciences, Faculty of Sciences, Amar Teleji Laghouat University, Laghouat, Algeria

    Abdelbaki Choucha

  2. Laboratory of Mathematics and Applied Sciences, Ghardaia University, Bounoura, Algeria

    Abdelbaki Choucha

  3. Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia

    Salah Boulaaras & Mohammad Alnegga

Authors
  1. Abdelbaki Choucha
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  2. Salah Boulaaras
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  3. Mohammad Alnegga
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Contributions

AC: writing original draft, Methodology, Resources, Methodology, formal analysis, Conceptualization; SB, AC: conceptualized, investigated, analyzed and validated the research while, SB, AC: formulated, investigated, reviewed and supervised, SB: Corresponding author, Supervision.

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Correspondence to Salah Boulaaras.

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Choucha, A., Boulaaras, S. & Alnegga, M. Local existence and blow up for the wave equation with nonlinear logarithmic source term and nonlinear dynamical boundary conditions combined with distributed delay. Afr. Mat. 35, 71 (2024). https://doi.org/10.1007/s13370-024-01212-6

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  • DOI: https://doi.org/10.1007/s13370-024-01212-6

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