No data available.

Please log in to see this content.

You have no subscription access to this content.

No metrics data to plot.

The attempt to load metrics for this article has failed.

The attempt to plot a graph for these metrics has failed.

The full text of this article is not currently available.

Hierarchy of conservation laws of diffusion-convection equations

### Abstract

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such systems. We also revise the notion of linear dependence of conservation laws and define the notion of local dependence of potentials. To construct conservation laws, we develop and apply the most direct method which is effective to use in the case of two independent variables. Admitting possibility of dependence of conserved vectors on a number of potentials, we generalize the iteration procedure proposed by Bluman and Doran-Wu for finding nonlocal (potential) conservation laws. As an example, we completely classify potential conservation laws (including arbitrary order local ones) of diffusion-convection equations with respect to the equivalence group and construct an exhaustive list of locally inequivalent potential systems corresponding to these equations.

© 2005 American Institute of Physics

Received 30 November 2004
Accepted 14 January 2005
Published online 15 March 2005

Acknowledgments:
The authors are grateful to V. Boyko, A. Nikitin, A. Sergyeyev, I. Yehorchenko, and A. Zhalij for useful discussions and interesting comments. Research of N.M.I. was supported by National Academy of Science of Ukraine in the form of the grant for young scientists. R.O.P. thanks Professor F. Ardalan and Dr. H. Eshraghi (School of Physics, Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran) for hospitality and support during the writing of this paper.

Article outline:

I. INTRODUCTION
II. BASIC DEFINITIONS AND STATEMENTS
III. EQUIVALENCE OF CONSERVATION LAWS
IV. DIRECT ITERATION METHOD OF FINDING CONSERVATION LAWS
V. TWO-DIMENSIONAL CASE
VI. LOCAL CONSERVATION LAWS OF DIFFUSION-CONVECTION EQUATIONS
VII. SIMPLEST POTENTIAL CONSERVATION LAWS OF DIFFUSION-CONVECTION EQUATIONS
VIII. POTENTIAL CONSERVATION LAWS OF LINEAR HEAT EQUATION
IX. POTENTIAL CONSERVATION LAWS OF NONLINEAR DIFFUSION-CONVECTION EQUATIONS
X. CONCLUSION

/content/aip/journal/jmp/46/4/10.1063/1.1865813

http://aip.metastore.ingenta.com/content/aip/journal/jmp/46/4/10.1063/1.1865813

Article metrics loading...

/content/aip/journal/jmp/46/4/10.1063/1.1865813

2005-03-15

2016-02-08

Full text loading...

###
Most read this month

Article

content/aip/journal/jmp

Journal

5

3

Commenting has been disabled for this content