Applied Mathematics and Mechanics

, Volume 28, Issue 11, pp 1503-1516

First online:

Schauder estimates for parabolic equation of bi-harmonic type

  • Yao Feng-ping 姚锋平Affiliated withLMAM, School of Mathematical Sciences, Peking University Email author 
  • , Zhou Shu-lin 周蜀林Affiliated withLMAM, School of Mathematical Sciences, Peking University

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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