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Functional Separable Solutions to Nonlinear Diffusion Equations by Group Foliation Method |
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| Authors: | HU Jia-Yi QU Chang-Zheng YIN Hui |
| Institution: | 1. Center for Nonlinear Studies, Northwest University, Xi'an 710069, China ;2. Department of Mathematics, Northwest University, Xi'an 710069, China ;3. Department of Mathematics, South-Central University of Nationalities, Wuhan 430074, China ;4. Wuhan Institute of Physics and Mathematics, the Chinese Academy of Sciences, Wuhan 430071, China |
| Abstract: | We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term: ut=(A(x)D(u)ux)x+B(x)Q(u), Ax≠0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained. |
| Keywords: | group foliation method functional separation of variable nonlinear diffusion equation symmetry group |
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