What question did this study set out to answer?

This work aims to explore a wave equation influenced by Balakrishnan-Taylor damping and logarithmic source terms. It seeks to understand global existence and energy behavior under various initial conditions.

August 3, 2026Journal of Applied Analysis & ComputationOpen Access

Qualitative Analysis of a Wave Equation With Balakrishnan-Taylor Damping and Logarithmic Source Terms

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Authors

NBN. Boumaza BGB. Gheraibia GLG. Liu

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Implication

Qualitative analysis investigates wave equation behavior in stable and unstable initial data sets, highlighting energy decay.

Key Points

This work aims to explore a wave equation influenced by Balakrishnan-Taylor damping and logarithmic source terms. It seeks to understand global existence and energy behavior under various initial conditions.
Analyzed the initial-boundary value problem for the wave equation.
Employed the potential well method along with logarithmic Sobolev inequalities.
Established energy decay and solution behavior in stable and unstable sets of initial data.
Demonstrated global existence and energy decay of solutions for stable initial data.
Showed that solutions blow up in infinite time for unstable initial data under certain energy conditions, E(0)<d and E(0)<0.
Provided insights into the long-term behavior dictated by the balance of damping effects and logarithmic nonlinearity.

Cite This Study

Boumaza et al. (2026) studied this question.

synapsesocial.com/papers/6a70406d75942ff7265e55fd https://doi.org/10.11948/20250330

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Qualitative Analysis of a Wave Equation With Balakrishnan-Taylor Damping and Logarithmic Source Terms

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Implication

Key Points

Cite This Study

Qualitative Analysis of a Wave Equation With Balakrishnan-Taylor Damping and Logarithmic Source Terms

Discussion

Member takes

Implication

Key Points

Cite This Study

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