Forced Burgers equation with sticky impulsion source

IF 0.9 Q2 MATHEMATICS
Florent Nzissila, Octave Moutsinga
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引用次数: 0

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.

带有粘性推进源的强制布尔格斯方程
我们考虑的是具有力((\partial _t u+\partial _x(u^2/2)=\nu \)的不粘性布尔格斯方程,其中初始数据\(u_0\)的不连续性被解释为力源。因此,\(\nu \)是(自相矛盾的)非加速粒子粘性动力学中的冲击力,其质量分布场是\(\partial _xu\)。这个力有它自己的动力学密度场(经历的推动力),其中w表示粘性粒子的速度场。沿着粘性粒子轨迹(t/mapsto X_t/),过程(t/mapsto \eta (X_t,t),u(X_t,t),w(X_t,t))都是后向马丁格尔。
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来源期刊
Afrika Matematika
Afrika Matematika MATHEMATICS-
CiteScore
2.00
自引率
9.10%
发文量
96
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