Analytic Solutions of a Class of Nonlinear Partial Differential Equations

ZHANG Hong-qing; DING Qi

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ZHANG Hong-qing, DING Qi. Analytic Solutions of a Class of Nonlinear Partial Differential Equations[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1268-1278.

Citation:

ZHANG Hong-qing, DING Qi. Analytic Solutions of a Class of Nonlinear Partial Differential Equations[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1268-1278.

Citation:

ZHANG Hong-qing, DING Qi. Analytic Solutions of a Class of Nonlinear Partial Differential Equations[J]. Applied Mathematics and Mechanics, 2008, 29(11): 1268-1278.

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Analytic Solutions of a Class of Nonlinear Partial Differential Equations

ZHANG Hong-qing,
DING Qi^1,2

Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116023, P. R. China

Received Date: 2008-08-25
Rev Recd Date: 2008-09-25
Publish Date: 2008-11-15

Abstract

Abstract

Firstly, an approach is presented for computing the adjoint operator vector of a class of nonlinear (i. e. partial-nonlinear) operator matrix by generalizing the method presented by Zhang et al. and the conjugate operators. Secondly, a united theory is given for solving a class of nonlinear (i. e. partial-nonlinear and including all linear) and non-homogeneous differential equations by the mathe-matics-mechanization method. In other words, a transformation is constructed by homogenization and triangulation which can reduce the original system to the simpler one which is diagonal. Finally, some practical applications are given in elasticity equations.
- AC=BD model,
- partial- nonlinear,
- adjoint,
- conjugate,
- plate and shell

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References(8)

References

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