Solutions to a Class of Nonlinear Strong-Damp Disturbed Evolution Equations

SHI Juan-rong; SHI Lan-fang; MO Jia-qi

doi:10.3879/j.issn.1000-0887.2014.09.010

Volume 35 Issue 9

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SHI Juan-rong, SHI Lan-fang, MO Jia-qi. Solutions to a Class of Nonlinear Strong-Damp Disturbed Evolution Equations[J]. Applied Mathematics and Mechanics, 2014, 35(9): 1046-1054. doi: 10.3879/j.issn.1000-0887.2014.09.010

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Solutions to a Class of Nonlinear Strong-Damp Disturbed Evolution Equations

doi: 10.3879/j.issn.1000-0887.2014.09.010

¹Anhui Technical College of Mechanical and Electrical Engineering, Wuhu, Anhui 241002, P.R.China;²College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, P.R.China;³Department of Mathematics, School of Mathematics & Computer Science,Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Funds: The National Natural Science Foundation of China(11202106)

Received Date: 2014-03-07
Rev Recd Date: 2014-06-20
Publish Date: 2014-09-15

Abstract

Abstract

Widely emerging in the fields of mathematics and mechanics, a class of 3rd-order nonlinear strong-damp disturbed partial differential evolution equations were studied. Firstly, a functional homotopic mapping was constructed to express the solution to the evolution equation in a form of power series with artificial parameters, which was substituted into the homotopic mapping to build a method of successive iteration for the solution to the nonlinear disturbed equation. Then the corresponding non-disturbed strong-damp evolution equation was analyzed with exact solution based on the theory of Fourier transform. Secondly, the found exact solution was used as the initial function of the homotopic mapping iteration, and the iteration expansion of the nonlinear disturbed equation was applied to solve the related equations with the Fourier transform method. Finally, both the exact and arbitrary-order approximate analytic solutions to the nonlinear strong-damp disturbed evolution equation were obtained. The proposed homotopic mapping method is proved to have the advantages of convenience and accuracy.
- evolution equation,
- perturbation,
- homotopic mapping

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References(23)

References

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