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Schauder estimates for parabolic equation of bi-harmonic type

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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.

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Authors and Affiliations

  1. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

    Yao Feng-ping  (姚锋平) & Zhou Shu-lin  (周蜀林)

Authors
  1. Yao Feng-ping  (姚锋平)
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  2. Zhou Shu-lin  (周蜀林)
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Corresponding author

Correspondence to Yao Feng-ping  (姚锋平).

Additional information

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)

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Yao, Fp., Zhou, Sl. Schauder estimates for parabolic equation of bi-harmonic type. Appl. Math. Mech.-Engl. Ed. 28, 1503–1516 (2007). https://doi.org/10.1007/s10483-007-1110-z

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  • DOI: https://doi.org/10.1007/s10483-007-1110-z

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2000 Mathematics Subject Classification

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