Applied Mathematics and Mechanics

, Volume 28, Issue 11, pp 1503–1516

Schauder estimates for parabolic equation of bi-harmonic type

  • Yao Feng-ping  (姚锋平)
  • Zhou Shu-lin  (周蜀林)

DOI: 10.1007/s10483-007-1110-z

Cite this article as:
Yao, F. & Zhou, S. Appl. Math. Mech.-Engl. Ed. (2007) 28: 1503. doi:10.1007/s10483-007-1110-z


Global Schauder estimates for the initial-value parabolic problem of the bi-harmonic type are proved, and the existence and uniqueness of the solutions in the suitable space are obtained. Similarly to the second-order case, first a formal expression of solutions by the Fourier transform is obtained, and then the regularity, uniqueness and existence of solutions using the potential theory and approximation argument are got. out approach is simple and straightforward.

Key words

bi-harmonic parabolic Schauder estimates existence uniqueness 

Chinese Library Classification


2000 Mathematics Subject Classification

35A05 35K25 35G05 

Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Yao Feng-ping  (姚锋平)
    • 1
  • Zhou Shu-lin  (周蜀林)
    • 1
  1. 1.LMAM, School of Mathematical SciencesPeking UniversityBeijingP. R. China

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