Matsumura-type Estimates and Global Solutions of a Fractional Wave Equation with Nonlocal Nonlinearity

2025 · doi:10.22541/au.176067733.34781838/v1
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Abstract

The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of ε u tt + u t + ( - Δ ) β u = 0 , u ( 0 , x ) = φ ( x ) , u t ( 0 , x ) = ψ ( x ) , which we derive particularly to observe the roles of ε and β in the long time behavior of solutions. Moreover, we apply these estimates to obtain local in time weak solutions, and global solutions, under the influence of a nonlocal non-power nonlinear term.
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Abstract

The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of ε u tt + u t + ( - Δ ) β u = 0, u ( 0, x ) = φ ( x ), u t ( 0, x ) = ψ ( x ), which we derive particularly to observe the roles of ε and β in the long time behavior of solutions. Moreover, we apply these estimates to obtain local in time weak solutions, and global solutions, under the influence of a nonlocal non-power nonlinear term. Supplementary Material File (mma-kirane-suleman.pdf) - Download - 258.53 KB Information & Authors Information Version history Peer review timeline Published Mathematical Methods in the Applied Sciences Version of Record15 Feb 2026Published Copyright This work is licensed under a Non Exclusive No Reuse License. Collection

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Authors Metrics & Citations Metrics Article Usage 219views 166downloads Citations Download citation Ibrahim Suleman, Mokhtar Kirane. Matsumura-type Estimates and Global Solutions of a Fractional Wave Equation with Nonlocal Nonlinearity. Authorea. 17 October 2025. DOI: https://doi.org/10.22541/au.176067733.34781838/v1 DOI: https://doi.org/10.22541/au.176067733.34781838/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.

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