Global Schauder estimates for the initial-value parabolic problem of the hi-harmonic type are proved, and the existence and uniqueness of the solutions in the suitable space are obtained. Similarly to the second-order...Global Schauder estimates for the initial-value parabolic problem of the hi-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.展开更多
基金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)the Key Project of Chinese Ministry of Education (No.306017)
文摘Global Schauder estimates for the initial-value parabolic problem of the hi-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.
