TY - JOUR
T1 - Lie Group Analysis for a Multispecies, Spatially Inhomogeneous,
T2 - Mutually Interacting Gas Mixture
AU - Azmy, Y. Y.
AU - Boffi, V. C.
AU - Mandrekas, J.
AU - Protopopescu, V.
AU - Azmy, Y. Y.
PY - 1992/2/1
Y1 - 1992/2/1
N2 - We consider systems of general nonlinear PDEs that arise in the extended kinetic theory of gases describing mixtures of spatially inhomogeneous, mutually interacting species. For general, autonomous, space-independent interaction laws, these systems are always invariant under the translation group. Via Lie group analysis methods, we show that for a Lotka-Volterra interaction law and three or more species, the system is invariant under a three-parameter group of transformations representing scaling, and translation in time and space. Moreover, the Lie group analysis shows that this is the only invariance group of the system.
AB - We consider systems of general nonlinear PDEs that arise in the extended kinetic theory of gases describing mixtures of spatially inhomogeneous, mutually interacting species. For general, autonomous, space-independent interaction laws, these systems are always invariant under the translation group. Via Lie group analysis methods, we show that for a Lotka-Volterra interaction law and three or more species, the system is invariant under a three-parameter group of transformations representing scaling, and translation in time and space. Moreover, the Lie group analysis shows that this is the only invariance group of the system.
UR - http://www.scopus.com/inward/record.url?scp=0011612173&partnerID=8YFLogxK
U2 - 10.1080/00411459208203525
DO - 10.1080/00411459208203525
M3 - Article
AN - SCOPUS:0011612173
SN - 0041-1450
VL - 21
SP - 119
EP - 131
JO - Transport Theory and Statistical Physics
JF - Transport Theory and Statistical Physics
IS - 1-2
ER -