Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to n...Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.展开更多
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 thi...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.展开更多
We study the functional separation of variables to the nonlinear heat equation： ut = （A（x）D（u）ux^n）x＋ B（x）Q（u）, Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables...We study the functional separation of variables to the nonlinear heat equation： ut = （A（x）D（u）ux^n）x＋ B（x）Q（u）, Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained.展开更多
文摘Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.
基金The project supported by National Natural Science Foundation of China under Grant No. 10371098 and the Program for New Century Excellent Talents in Universities under Grant No. NCET-04-0968
文摘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.
基金National Natural Science Foundation of China under Grant No.10671156the Program for New Century Excellent Talents in Universities under Grant No.NCET-04-0968
文摘We study the functional separation of variables to the nonlinear heat equation： ut = （A（x）D（u）ux^n）x＋ B（x）Q（u）, Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained.
