摘要
The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.
The inhomogeneous nonlinear difusion equation is studied by invariant subspace and conditional Lie-Bcklund symmetry methods.It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary diferential equations,which is equivalent to a kind of higher-order conditional Lie-Bcklund symmetries of the equations.As a consequence,a number of new solutions to the inhomogeneous nonlinear difusion equations are constructed explicitly or reduced to solving fnite-dimensional dynamical systems.
基金
supported by National Natural Science Foundation of China for Distinguished Young Scholars(Grant No.10925104)
the PhD Programs Foundation of Ministry of Education of China(Grant No.20106101110008)
the United Funds of NSFC and Henan for Talent Training(Grant No.U1204104)
