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This is a Quantitative Study study.

October 13, 2025Open Access

On the logarithmic correction of transition fronts in shifting environments

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The study reveals the location of the spreading front in unbounded domains and environments with discontinuities.
It shows that convergence to traveling wave profiles occurs through innovative construction methods based on prior work.
This approach employs gluing techniques to develop super/subsolutions, enhancing understanding of wave dynamics.
Findings may enable better modeling of phenomena where environment shifts affect wave propagation and convergence.

Implication

Analysis finds the spreading front and wave profile in shifting environments, indicating implications for mathematical modeling.

Abstract

In this paper, we investigate the location of the spreading front and convergence to traveling wave profile of solutions to the Fisher-KPP equation in the following two cases: (i) in unbounded domains with an expanding boundary; (ii) on the real line where the environment function has a shifting jump discontinuity. Our approach is based on extending ideas in Bramson's seminal work in 1983, and applying gluing technique to construct super/subsolutions.

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Cite This Study

Lam et al. (2025) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec094f5 https://doi.org/10.48550/arxiv.2509.11521

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Implication

Analysis finds the spreading front and wave profile in shifting environments, indicating implications for mathematical modeling.

On the logarithmic correction of transition fronts in shifting environments

Key Points

Implication

Abstract

Discussion

Cite This Study

On the logarithmic correction of transition fronts in shifting environments

Key Points

Implication

Abstract

Discussion

Cite This Study

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