Conservation Laws of Variable Coefficient Diffusion-Convection Equations

Simple item page
dc.creatorIvanova, N. M.
dc.creatorPopovych, R. O.
dc.creatorSophocleous, C.
dc.date2005-05-05
dc.date.accessioned2026-07-07T04:32:05Z
dc.date.available2026-07-07T04:32:05Z
dc.descriptionWe study local conservation laws of variable coefficient diffusion-convection equations of the form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$. The main tool of our investigation is the notion of equivalence of conservation laws with respect to the equivalence groups. That is why, for the class under consideration we first construct the usual equivalence group $G^{\sim}$ and the extended one $\hat G^{\sim}$ including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group $\hat G^{\sim}$ has interesting structure since it contains a non-trivial subgroup of gauge equivalence transformations. Then, using the most direct method, we carry out two classifications of local conservation laws up to equivalence relations generated by $G^{\sim}$ and $\hat G^{\sim}$, respectively. Equivalence with respect to $\hat G^{\sim}$ plays the major role for simple and clear formulation of the final results.
dc.description7 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0505015
dc.identifierhttp://arxiv.org/abs/math-ph/0505015
dc.identifierProceedings of 10th International Conference in MOdern GRoup ANalysis (Larnaca, Cyprus, 2004), 107-113
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58061
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.subject35K57; 35A30
dc.titleConservation Laws of Variable Coefficient Diffusion-Convection Equations
dc.typetext

Files

Collections

arXiv