Abstract：The partial group analysis of a nonhomogeneous integro-differential Smoluchowski equation with a source term and homogeneous kernel function is investigated by use of the method of preliminary group classification in this paper. Firstly， the symmetries， complete group classification and optimal systems of subalgebras of homogeneous integro-differential Smoluchowski equation with homogeneous kernel are obtained using the method of developed Lie group analysis. Secondly， the determining equation， general solutions to determining equation， invariant solutions and explicit analytical solutions for the corresponding nonhomogeneous integro-differential Smoluchowski equation with a source term and homogeneous kernel function are presented by the method of preliminary group classification. Finally， the obtained results have demonstrated that the method of preliminary group classification can be applied not only to partial differential equations， but also to integro-differential equations.
林府标,张千宏. 含源项的Smoluchowski方程的预李群分类[J]. 华中师范大学学报(自然科学版), 2020, 54(5): 749-757.
LIN Fubiao,ZHANG Qianhong. Preliminary group classification of Smoluchowski equation with a source term. journal1, 2020, 54(5): 749-757.
2020, Vol. 54 
