Analytic solutions of a class of nonlinear partial differential equations

作者：Zhang Hong qing^*; Ding Qi

来源：Applied Mathematics and Mechanics, 2008, 29(11): 1399-1410.

DOI：10.1007/s10483-008-1102-z

• AC = BD model
• partial-nonlinear
• adjoint
• conjugate
• plate and shell
• O175
• 2
• 35A08

An approach is presented for computing the adjoint operator vector of a class of nonlinear (that is, partial-nonlinear) operator matrices by using the properties of conjugate operators to generalize a previous method proposed by the author. A unified theory is then given to solve a class of nonlinear (partial-nonlinear and including all linear) and non-homogeneous differential equations with a mathematical mechanization method. In other words, a transformation is constructed by homogenization and triangulation, which reduces the original system to a simpler diagonal system. Applications are given to solve some elasticity equations.

• 出版日期2008-11
• 单位大连理工大学