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Existence and uniqueness of global solutions of onR 2

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An Erratum to this article was published on 01 October 1998

Abstract

In this paper, we consider the solutions of the nonlinear Schrödinger equations ∂u/∂t−iΔu+|u|p u=f andu(x,0)=u 0(x), whereu is defined onR +×R 2. We prove the existence and uniqueness of global weak solutions of the above equations. Lastly, we consider the special case:p=2, and we obtain the strong solutions.

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References

  1. J.L. Lions. Quelques Méthodes de Résolution des Problèm aux Limites Nonlinéaires. DONOD, GAUTHIER-VILLARS, Paris 1969.

    Google Scholar 

  2. Ding Xiaxi, Luo Peizhu and Li Yanyan. The Solvability of Nonlinear Parabolic Equation in Ba Space.J. of Central Teachers College (Natural Science Edition), 1985, 2: 1–9.

    Google Scholar 

  3. Li Congming. Global Properties of The Solutions of Nonlinear Schrödinger Equations on a Bounded Domain.J. Sys. Sci. & Math. Scis., 1984, 4(2): 160–164.

    Google Scholar 

  4. Li Daqian. Nonlinear Evolutional Equations. Science Press, Beijing, 1989.

    Google Scholar 

  5. Yao Jingqi. Time Decay of Solutions to a Nonlinear Schrödinger Equation in an Exterior Domain inR 2.Nonlinear Analysis, 1992, 19: 563–571.

    Google Scholar 

  6. M. Tsutsumi. On Smooth Solutions to the Initial-boundary Value Problem for the Nonlinear Schrödin -ger Equation in Two Space Dimensions.Nonlinear Analysis, 1989, 13: 1051–1056.

    Google Scholar 

  7. L. Segal. Nonlinear Semi-groups.Ann. Math., 1963, 78: 339–364.

    Google Scholar 

  8. H. Brézis and T. Gallouet. Nonlinear Schrödinger Evolution Equations.Nonlinear Analysis, 1980, 4: 677–681.

    Google Scholar 

  9. Yao Jingqi. The Solutions of One Type of Nonlinear Schrödinger Equations.Chinese Annals of Mathematics, 1986, 7A(4): 413–422 (in Chinese).

    Google Scholar 

  10. R. Temam. Navier-Stokes Equations. Elasevier Science Publishers B.V., Netherlands, 1985.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Capital Normal University, 100037, Beijing, China

    Jiu Quansen

  2. Institute of Applied Mathematics, the Chinese Academy of Sciencfles, 100080, Beijing, China

    Liu Jun

Authors
  1. Jiu Quansen
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  2. Liu Jun
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An erratum to this article is available at http://dx.doi.org/10.1007/BF02683820.

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Jiu, Q., Liu, J. Existence and uniqueness of global solutions of onR 2 . Acta Mathematicae Applicatae Sinica 13, 414–424 (1997). https://doi.org/10.1007/BF02009551

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  • DOI: https://doi.org/10.1007/BF02009551

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