TY - JOUR
A2 - Khalique, Chaudry M.
AU - Mindu, N.
AU - Mason, D. P.
PY - 2014
DA - 2014/05/04
TI - Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity
SP - 585167
VL - 2014
AB - The derivation of conservation laws for the magma equation using the multiplier method for both the power law and exponential law relating the permeability and matrix viscosity to the voidage is considered. It is found that all known conserved vectors for the magma equation and the new conserved vectors for the exponential laws can be derived using multipliers which depend on the voidage and spatial derivatives of the voidage. It is also found that the conserved vectors are associated with the Lie point symmetry of the magma equation which generates travelling wave solutions which may explain by the double reduction theorem for associated Lie point symmetries why many of the known analytical solutions are travelling waves.
SN - 1085-3375
UR - https://doi.org/10.1155/2014/585167
DO - 10.1155/2014/585167
JF - Abstract and Applied Analysis
PB - Hindawi Publishing Corporation
KW -
ER -