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arXiv · 2606.00905

On the wave equation with logarithmic damping: wellposedness, blow-up and numerical analysis

Salim Messaoudi·Mohammad Kafini·Mostafa Zahri
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Abstract

In this work, we are concern with the wave equation subjected to a nonlinear feedback of logarithmic type and nonlinear polynomial source. To achieve a comprehensive understanding of this novel damping mechanism, we start with studying the well-posedness and the uniqueness of the problem. Then we establish the blow-up result of the problem under suitable initial data with negative initial energy and critical exponent of the source term. Finally, we present a brief numerical study and examples that support our result.

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Salim Messaoudi, Mohammad Kafini, Mostafa Zahri. 2026-05-30. On the wave equation with logarithmic damping: wellposedness, blow-up and numerical analysis. https://arxiv.org/abs/2606.00905

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