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Elliptic and Parabolic Equations

  • Chapter
Partial Differential Equations in China

Part of the book series: Mathematics and Its Applications ((MAIA,volume 288))

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Abstract

This article provides a brief servey of the results on the partial differential equations and systems of elliptic and parabolic types contributed by the Chinese mathematicians in the period from 1950 to 1980. The major contributions in this period are summarized in the following topics.

  1. 1

    On the definition of elliptic systems

  2. 2

    New prototypes of initial and boundary value problems

  3. 3

    Schauder estimates for solutions to high order parabolic equations and systems

  4. 4

    Boundary value problems of first order elliptic systems with two variables via the theory of generalized analytic functions

  5. 5

    Linear boundary value problems of the other types

  6. 6

    Asymptotic behavior of solutions to parabolic equations

  7. 7

    Nonlinear parabolic equations of second order

  8. 8

    Calcilus of variations with strong nonlinearities

  9. 9

    Subsonic flows in high dimensions

In the field of elliptic and parabolic equations (or systems), the early researehes of Chinese mathematicians laid emphasis on classification of equations and various linear and nonlinear prescribed boundary value problems. Abrief introduction is as folIows.

1991 Mathematics Subject Classification: 35J25, 35J65, 35K60

Supported by NNSF of China and Foundation of Science of Zhejiang Province

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Author information

Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, China

    Guangcang Dong

Authors
  1. Guangcang Dong
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Editor information

Editors and Affiliations

  1. Fudan University, Shanghai, China

    Chaohao Gu

  2. Institute of Applied Mathematics, Academia Sinica, Beijing, China

    Xiaxi Ding

  3. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Chung-Chun Yang

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© 1994 Springer Science+Business Media Dordrecht

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Dong, G. (1994). Elliptic and Parabolic Equations. In: Gu, C., Ding, X., Yang, CC. (eds) Partial Differential Equations in China. Mathematics and Its Applications, vol 288. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1198-0_3

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  • DOI: https://doi.org/10.1007/978-94-011-1198-0_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4524-7

  • Online ISBN: 978-94-011-1198-0

  • eBook Packages: Springer Book Archive

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