Convex hulls, Sticky particle dynamics and Pressure-less gas system

Moutsinga, Octave. "Convex hulls, Sticky particle dynamics and Pressure-less gas system." Annales mathématiques Blaise Pascal 15.1 (2008): 57-80. <http://eudml.org/doc/10553>.

@article{Moutsinga2008,
abstract = {We introduce a new condition which extends the definition of sticky particle dynamics to the case of discontinuous initial velocities $u_0$ with negative jumps. We show the existence of a stochastic process and a forward flow $\phi $ satisfying $X_\{s+t\} = \phi (X_s,t,P_s,u_s)$ and $\mathrm\{d\}X_t =\mathrm\{E\}[ u_0(X_0)/X_t]\mathrm\{d\}t$, where $P_s=PX_s^\{-1\}$ is the law of $X_s$ and $u_s(x) = \mathrm\{E\}[ u_0(X_0)/X_s = x]$ is the velocity of particle $x$ at time $s\ge 0$. Results on the flow characterization and Lipschitz continuity are also given.Moreover, the map $(x,t)\mapsto M(x,t):= P(X_t\le x)$ is the entropy solution of a scalar conservation law $\partial _tM + \partial _x(A(M)) = 0$ where the flux $A$ represents the particles momentum, and $\big (P_t,\,u_t,\; t &gt;0\big )$ is a weak solution of the pressure-less gas system of equations of initial datum $P_0, u_0$.},
affiliation = {Université des Sciences et Techniques de Masuku Faculté des Sciences - Dpt Mathématiques et Informatique BP 943 Franceville, Gabon.},
author = {Moutsinga, Octave},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Convex hull; sticky particles; forward flow; stochastic differential equation; scalar conservation law; pressure-less gas system; Hamilton-Jacobi equation},
language = {eng},
month = {1},
number = {1},
pages = {57-80},
publisher = {Annales mathématiques Blaise Pascal},
title = {Convex hulls, Sticky particle dynamics and Pressure-less gas system},
url = {http://eudml.org/doc/10553},
volume = {15},
year = {2008},
}

TY - JOUR
AU - Moutsinga, Octave
TI - Convex hulls, Sticky particle dynamics and Pressure-less gas system
JO - Annales mathématiques Blaise Pascal
DA - 2008/1//
PB - Annales mathématiques Blaise Pascal
VL - 15
IS - 1
SP - 57
EP - 80
AB - We introduce a new condition which extends the definition of sticky particle dynamics to the case of discontinuous initial velocities $u_0$ with negative jumps. We show the existence of a stochastic process and a forward flow $\phi $ satisfying $X_{s+t} = \phi (X_s,t,P_s,u_s)$ and $\mathrm{d}X_t =\mathrm{E}[ u_0(X_0)/X_t]\mathrm{d}t$, where $P_s=PX_s^{-1}$ is the law of $X_s$ and $u_s(x) = \mathrm{E}[ u_0(X_0)/X_s = x]$ is the velocity of particle $x$ at time $s\ge 0$. Results on the flow characterization and Lipschitz continuity are also given.Moreover, the map $(x,t)\mapsto M(x,t):= P(X_t\le x)$ is the entropy solution of a scalar conservation law $\partial _tM + \partial _x(A(M)) = 0$ where the flux $A$ represents the particles momentum, and $\big (P_t,\,u_t,\; t &gt;0\big )$ is a weak solution of the pressure-less gas system of equations of initial datum $P_0, u_0$.
LA - eng
KW - Convex hull; sticky particles; forward flow; stochastic differential equation; scalar conservation law; pressure-less gas system; Hamilton-Jacobi equation
UR - http://eudml.org/doc/10553
ER -