Articles

NOTE ON AN OPEN PROBLEM OF HIGHER ORDER NONLINEAR EVOLUTION EQUATIONS

  • Tujin Kim ,
  • CHANG Qian-Shun ,
  • XU Jing
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  • 1.Institute of Mathematics, Academy of Sciences of DPR of Korea, Pyonyang, DPR of Korea; 2.Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China; 3.School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Received date: 2011-01-28

  Online published: 2012-11-20

Supported by

The first author´s research is supported by TWAS, UNESO and AMSS in Chinese Academy. The research of the third author is partially supported by NSFC (11001239).

Abstract

In view of a new idea on initial conditions, an open problem of nonlinear evolution equations with higher order, which was given by J. L. Lions, is solved. Effect of our results is shown on an example.

Cite this article

Tujin Kim , CHANG Qian-Shun , XU Jing . NOTE ON AN OPEN PROBLEM OF HIGHER ORDER NONLINEAR EVOLUTION EQUATIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(6) : 2369 -2376 . DOI: 10.1016/S0252-9602(12)60185-4

References

[1] Gajewski H, Grëger K, Zacharias K. Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Mathematische Nachrichten Academic-Verlag, 1975, 67(22): 4–4

[2] Larikin N A, Novikov V A, Yanenko N N. Equations of nonclassical types and their applications in continuum mechanics//Current Problems in Numerical and Applied Mathematics (Novosibirsk, 1981). Novosibirsk: Nauka, Sibirsk Otdel, 1983: 22–27 (Russian)

[3] Larikin N A, Novikov V A, Yanenko N N. Nonlinear Equations of Variable Type. Novosibirsk: Nauka, 1983 (Russian)

[4] Lions J L. Quelques M´ethodes de R´esolution des Problemes aux Limites non Linéaires. Paris: Dunod, 1969, 76

[5] Zhao Y D, Li K T. Existence of global attractors for a nonlinear evolution equation in Sobolev space Hk. Acta Math Sci, 2009, 29B(5): 1165–1172

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