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- W4383860478 abstract "We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are physically relevant ones as opposed to the uniform tumbling kernel which is widely considered in the literature to reduce the complexity of the mathematical analysis. We consider two cases: (i) the tumbling kernel depends on the angle between pre- and post-tumbling velocities, (ii) the velocity space is unbounded and the post-tumbling velocities follow the Maxwellian velocity distribution. We prove that the probability density distribution of bacteria converges to an equilibrium distribution with explicit (exponential for (i) and algebraic for (ii)) convergence rates, for any probability measure initial data. To the best of our knowledge, our results are the first results concerning the long-time behaviour of run and tumble equations with non-uniform tumbling kernels." @default.
- W4383860478 created "2023-07-11" @default.
- W4383860478 creator A5023983461 @default.
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- W4383860478 date "2023-07-07" @default.
- W4383860478 modified "2023-09-27" @default.
- W4383860478 title "Trend to equilibrium for run and tumble equations with non-uniform tumbling kernels" @default.
- W4383860478 doi "https://doi.org/10.48550/arxiv.2307.03469" @default.
- W4383860478 hasPublicationYear "2023" @default.
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