Memory effects in measure transport equations

Fabio Camilli; Raul De Maio

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arXiv · 1806.10331

Memory effects in measure transport equations

Fabio Camilli·Raul De Maio

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Abstract

Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the time-derivative with power-law kernels, are typical for memory effects in complex systems. In this paper we consider a nonlinear transport equation with a fractional time-derivative. We provide a well-posedness theory for weak measure solutions of the problem and an integral formula which generalizes the classical push-forward representation formula to this setting.

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Fabio Camilli, Raul De Maio. 2018-06-27. Memory effects in measure transport equations. https://arxiv.org/abs/1806.10331

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