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AIMS Mathematics
Article . 2024 . Peer-reviewed
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AIMS Mathematics
Article . 2024
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Existence and stability results of nonlinear swelling equations with logarithmic source terms

Authors: Mohammad Kafini; Mohammad M. Al-Gharabli; Adel M. Al-Mahdi;

Existence and stability results of nonlinear swelling equations with logarithmic source terms

Abstract

<abstract><p>We considered a swelling porous-elastic system characterized by two nonlinear variable exponent damping and logarithmic source terms. Employing the Faedo-Galerkin method, we established the local existence of weak solutions under suitable assumptions on the variable exponents functions. Furthermore, we proved the global existence utilizing the well-depth method. Finally, we established several decay results by employing the multiplier method and the Logarithmic Sobolev inequality. To the best of our knowledge, this represents the first study addressing swelling systems with logarithmic source terms.</p></abstract>

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Keywords

logarithmic sobolev inequality, well-depth method, QA1-939, swelling system, general decay, faedo-galerkin method, variable exponents, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
gold