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数学与物理学

具有分数阶非线性项的表面生长模型在Besov空间中解的局部存在性和唯一性

  • 王庆恺 ,
  • 吴刚
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  • 中国科学院大学数学科学学院,北京 100049

收稿日期: 2024-04-01

  录用日期: 2024-05-17

  网络出版日期: 2023-05-10

基金资助

国家自然科学基金(11771423)

Local existence and uniqueness in Besov spaces for the solution of a surface growth model with fractional power nonlinear term

  • Qingkai WANG ,
  • Gang WU
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  • School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing,100049,China

Received date: 2024-04-01

  Accepted date: 2024-05-17

  Online published: 2023-05-10

摘要

研究初值为 h0 的如下一维四阶非线性方程的柯西问题:th+x4h+x2xhα=0,其中 α 是大于等于5的实数。通过对相应线性方程和非线性项的精细估计,结合Littlewood-Paley理论、双模方法以及压缩映射原理,在非齐次Besov空间中得到了方程的局部适定性结果。

本文引用格式

王庆恺 , 吴刚 . 具有分数阶非线性项的表面生长模型在Besov空间中解的局部存在性和唯一性[J]. 中国科学院大学学报, 2026 , 43(3) : 289 -295 . DOI: 10.7523/j.ucas.2023.052

Abstract

In this paper, we study the Cauchy problem for the 4-th order nonlinear equation th+x4h+x2xhα=0 in one dimension for the initial data h0 where α5 and αR. Making use of some subtle estimates of the corresponding linear equation and the nonlinear term, Littlewood-Paley theory, two-norm method, and contraction mapping principle, we obtain the local well-posedness result in nonhomogeneous Besov spaces.

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