TY - JOUR

T1 - Large time concentrations for solutions to kinetic equations with energy dissipation

AU - Jabin, Pierre Emmanuel

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2000

Y1 - 2000

N2 - We consider the solutions to a kinetic equation which kinetic energy converges to zero fast enough. We prove that they concentrate near the speed zero and converge towards a measure which is a product of a measure on the spacial coordinates and a Dirac mass on the speed coordinates. The difficult point here is that the full solution converges since we do not know any characterisation of the limit problem for the spatial density. We give two results of this kind, depending on the regularity of the solution, and on the assumptions. Finally we present an example of equation which describes the interactions of particles in a flow and where these theorems apply.

AB - We consider the solutions to a kinetic equation which kinetic energy converges to zero fast enough. We prove that they concentrate near the speed zero and converge towards a measure which is a product of a measure on the spacial coordinates and a Dirac mass on the speed coordinates. The difficult point here is that the full solution converges since we do not know any characterisation of the limit problem for the spatial density. We give two results of this kind, depending on the regularity of the solution, and on the assumptions. Finally we present an example of equation which describes the interactions of particles in a flow and where these theorems apply.

UR - http://www.scopus.com/inward/record.url?scp=0039004085&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039004085&partnerID=8YFLogxK

U2 - 10.1080/03605300008821523

DO - 10.1080/03605300008821523

M3 - Article

AN - SCOPUS:0039004085

SN - 0360-5302

VL - 25

SP - 541

EP - 557

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 3-4

ER -