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The asymptotic theory of initial value problems for semilinear pertubed wave equations in two space dimensions

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Abstract

The asymptotic theory of initial value problems for semilinear ware equations in two space dimensions was dealt with. The well-posedness and vaildity of formal approximations on a long time scale were discussed in the twice continuous classical space. These results describe the behavior of long time existence for the validity of formal approximations. And an application of the asymptotic theory is given to analyze a special wave equation in two space dimensions.

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References

  1. Van Horssen W T. An asymptotic theory for a class of initial boundary value problems for weakly nonlinear wave equation with an application to a model of the galloping oscillation of overhead transmission lines[J].SIAM, J Appl Math, 1988,48(6):1227–1243.

    Article  MATH  MathSciNet  Google Scholar 

  2. Van Horssen W T, Van Der Burgh A H P. On initial boundary value problems for weakly semilinear telegraph equations: asymptotic theory and application[J].SIAM J Appl Math, 1988,48 (4):719–737.

    Article  MATH  MathSciNet  Google Scholar 

  3. Van Horssen W T. Asymptotics for a class of semilinear hyperbolic equations with an application to a problem with a quadratic nonlinearity[J].Nonlinear Analysis, Theory, Methods and Application, 1992,19(6):501–503.

    Article  MATH  MathSciNet  Google Scholar 

  4. Blom C J, Van Der Burgh A H P. Validity of Approximations for time perodic solutions of a forced nonlinear hyperbolic differential equation[J].Applicable Analysis, 1994,52(4):155–176.

    MATH  MathSciNet  Google Scholar 

  5. LAI Shao-yong. The asymptotic theory of solutions for a perturbed telegraph wave equation and its application[J].Applied Mathematics and Mechanics (English Edition), 1997,18(7):657–662.

    Google Scholar 

  6. LAI Shao-yong, MU Chun-lai. The asymptotic theory of initial value problems for semilinear wave equations in three space dimensions[J].Appl Math-JCU, 1997,12B(4):321–332.

    Google Scholar 

  7. Guenther Ronald B, Lee John W.Partial Differential Equations of Mathematical Physics and Integral Equations[M]. New Jersey: Prentice-Hall, 1988.

    Google Scholar 

  8. Kôji Kubota. Existence of a global solution to a semilinear wave equations with initial data of noncompact support in low space dimensions[J].Hokkaido Math Journal, 1993,22(1):123–180.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, 610066, Chengdu, China

    Lai Shao-yong

  2. Department of Technology, Xichang Teacher's College, 630025, Xichang, Sichuan, China

    Fu Qing-long

Authors
  1. Lai Shao-yong
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  2. Fu Qing-long
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Additional information

Communicated by JIANG Fu-ru

Foundation item: Sichuan Youth Foundation (1999-09)

Biography: LAI Shao-yong (1965−), Associate Professor

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Shao-yong, L., Qing-long, F. The asymptotic theory of initial value problems for semilinear pertubed wave equations in two space dimensions. Appl Math Mech 24, 82–91 (2003). https://doi.org/10.1007/BF02439381

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  • DOI: https://doi.org/10.1007/BF02439381

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