Physics – Mathematical Physics
Scientific paper
2006-05-31
J. Math. Anal. Appl. 330 (2007) 1363-1386
Physics
Mathematical Physics
22 pages
Scientific paper
10.1016/j.jmaa.2006.08.056
A class of variable coefficient (1+1)-dimensional nonlinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u^nu_x)_x+h(x)u^m$ is investigated. Different kinds of equivalence groups are constructed including ones with transformations which are nonlocal with respect to arbitrary elements. For the class under consideration the complete group classification is performed with respect to convenient equivalence groups (generalized extended and conditional ones) and with respect to the set of all local transformations. Usage of different equivalences and coefficient gauges plays the major role for simple and clear formulation of the final results. The corresponding set of admissible transformations is described exhaustively. Then, using the most direct method, we classify local conservation laws. Some exact solutions are constructed by the classical Lie method.
Johnpillai A. G.
Popovych Roman O.
Sophocleous Christodoulos
Vaneeva Olena O.
No associations
LandOfFree
Enhanced Group Analysis and Conservation Laws of Variable Coefficient Reaction-Diffusion Equations with Power Nonlinearities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Enhanced Group Analysis and Conservation Laws of Variable Coefficient Reaction-Diffusion Equations with Power Nonlinearities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Enhanced Group Analysis and Conservation Laws of Variable Coefficient Reaction-Diffusion Equations with Power Nonlinearities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-711430