YAO Feng-ping, ZHOU Shu-lin. Schauder Estimates for the Parabolic Equation of the Bi-Harmonic Type[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1340-1352.
Citation: YAO Feng-ping, ZHOU Shu-lin. Schauder Estimates for the Parabolic Equation of the Bi-Harmonic Type[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1340-1352.

Schauder Estimates for the Parabolic Equation of the Bi-Harmonic Type

  • Received Date: 2006-10-23
  • Rev Recd Date: 2007-08-20
  • Publish Date: 2007-11-15
  • Global Schauder estimates for the initial-value parabolic problem of the bi-harmonic type were proved. The existence and uniqueness of the solutions in the suitable space were obtained. Similarly to the second-order case, a fomal expression of solutions by the Fourier transform was obtained. Then the regularity, uniqueness, existence of solutions using the potential theory and approximation argument were got. The approach is simple and straightforward.
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