A solution to the problem of invariants for parabolic equations
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences2009 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, Vol. 14, no 6, 2551-2558 p.Article in journal (Refereed) Published
The article is devoted to the Solution Of the invariants problem for the one-dimensional parabolic equations written in the two-coefficient canonical form used recently by N.H. Ibragimov: u(t) - u(xx) + a (t, x)u(x) + c(t, x)u = 0. A simple invariant condition is obtained for determining all equations that are reducible to the heat equation by the general group of equivalence transformations. The solution to the problem of invariants is given also in the one-coefficient canonical u(t) - u(xx) + c(t, x)u = 0. One of the main differences between these two canonical forms is that the equivalence group for the two-coefficient form contains the arbitrary linear transformation of the dependent variable whereas this group for the one-coefficient form contains only a special type of the linear transformations of the dependent variable. (C) 2008 Elsevier B.V. All rights reserved.
Place, publisher, year, edition, pages
AMSTERDAM: ELSEVIER SCIENCE BV , 2009. Vol. 14, no 6, 2551-2558 p.
Parabolic equations, Equivalent equations, Semi-invariant, Invariants
IdentifiersURN: urn:nbn:se:bth-8220DOI: 10.1016/j.cnsns.2008.10.007ISI: 000263590700007Local ID: oai:bth.se:forskinfo3929325A8425F260C12575B00020AEFBOAI: oai:DiVA.org:bth-8220DiVA: diva2:835909