Abstract
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.
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(Contributed by ZHANG Hong-qing)
Project supported by the National Basic Research Program of China (973 Program) (No. 2004CB318000)
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Zhang, Hq., Ding, Q. Analytic solutions of a class of nonlinear partial differential equations. Appl. Math. Mech.-Engl. Ed. 29, 1399–1410 (2008). https://doi.org/10.1007/s10483-008-1102-z
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DOI: https://doi.org/10.1007/s10483-008-1102-z