Applied Mathematics and Mechanics (English Edition) ›› 2007, Vol. 28 ›› Issue (11): 1503-1516 .doi: https://doi.org/10.1007/s10483-007-1110-z

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Schauder estimates for parabolic equation of bi-harmonic type

YAO Feng-ping, ZHOU Shu-lin   

  1. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China
  • Received:2006-10-23 Revised:2007-07-24 Online:2007-11-18 Published:2007-11-18
  • Contact: YAO Feng-ping

Abstract: 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.

2010 MSC Number: 

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