Weak self-adjointness and conservation laws for a porous medium equation

• Published in: Communications in nonlinear science & numerical simulation Vol. 17; no. 6; pp. 2342 - 2349
• Main Author: Gandarias, M.L.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2012
• Subjects: Conservation laws; Partial differential equations; Quasi self-adjointness; Self-adjointness; Symmetries; Weak self-adjointness; Conservation laws; Self-adjointness; Symmetries; Partial differential equations; Quasi self-adjointness; Weak self-adjointness
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2011.10.020

► We find the class of porous medium equations which are quasi self-adjoint. ► We determine the class of equations that are not quasi self-adjoint but are weak self-adjoint. ► We derive some new non-trivial conservation laws for these equations. The concepts of self-adjoint and quasi self-adjoint equations were introduced by Ibragimov (2006, 2007) [4,7]. In Ibragimov (2007) [6] a general theorem on conservation laws was proved. In Gandarias (2011) [3] we generalized the concept of self-adjoint and quasi self-adjoint equations by introducing the definition of weak self-adjoint equations. In this paper we find the subclasses of weak self-adjoint porous medium equations. By using the property of weak self-adjointness we construct some conservation laws associated with symmetries of the differential equation.