Schauder estimates for parabolic equation of bi-harmonic type. (English) Zbl 1231.35092
Summary: 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 shown. Our approach is simple and straightforward.
MSC:
| 35K25 | Higher-order parabolic equations |
| 35G05 | Linear higher-order PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
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