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Forced Burgers equation with sticky impulsion source

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Abstract

We consider the inviscid Burgers equation with force \(\partial _t u+\partial _x(u^2/2)=\nu \), where the discontinuities of initial datum \(u_0\) are interpreted as force sources. Thence, \(\nu \) is the force of shocks in a sticky dynamics of (paradoxically) non accelerated particles, whose the mass distribution field is \(\partial _xu\). The force has its own dynamics of density field \(\eta =u-w\) (the experienced impulsion), where w denotes the sticky particle velocity field. Along the sticky particle trajectory \(t\mapsto X_t\), the processes \(t\mapsto \eta (X_t,t),u(X_t,t),w(X_t,t)\) are backward martingales.

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  1. Unité de Recherches en Mathématiques et Informatique - Dpt Mathématiques et Informatique, Faculté des Sciences, Université des Sciences et Techniques de Masuku, BP 943, Franceville, Gabon

    Florent Nzissila & Octave Moutsinga

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  1. Florent Nzissila
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  2. Octave Moutsinga
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Correspondence to Octave Moutsinga.

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Nzissila, F., Moutsinga, O. Forced Burgers equation with sticky impulsion source. Afr. Mat. 35, 11 (2024). https://doi.org/10.1007/s13370-023-01150-9

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