, Volume 28, Issue 11, pp 1503-1516

Schauder estimates for parabolic equation of bi-harmonic type

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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.

Communicated by GUO Mao-zheng
Project supported by the Major State Basic Research Development Program of China (973 Program) (No. 2006CB705700), the National Natural Science Foundation of China (No. 60532080), and the Key Project of Chinese Ministry of Education (No. 306017)