Scholarlink

In this chapter, we study the inverse problem for the fractional semilinear equation with the exterior Dirichlet data of the form \(\displaystyle \begin {cases} (-\varDelta )^{s}u+a(x,u)=0 & \mbox{ in }\varOmega ,\\ u=f & \mbox{ in }\varOmega _{e}, \end {cases} \) where \(s\in (0,1)\) . A standard technique to handle nonlinear equations is to differentiate the equation to obtain a useful linear equation, and there are various ways for this purpose. We introduce higher-order linearization method so that one can prove the global uniqueness of certain nonlinear equations. Moreover, thanks to the nonlocality, we can also demonstrate a uniqueness result, without using any linearization scheme.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Inverse Problems for Fractional Semilinear Elliptic Equations

  • 章节

  • 发表日期：

    2025年

查看全文
  • Yi-Hsuan Lin,
  • Hongyu Liu

摘要

In this chapter, we study the inverse problem for the fractional semilinear equation with the exterior Dirichlet data of the form \(\displaystyle \begin {cases} (-\varDelta )^{s}u+a(x,u)=0 & \mbox{ in }\varOmega ,\\ u=f & \mbox{ in }\varOmega _{e}, \end {cases} \) where \(s\in (0,1)\) . A standard technique to handle nonlinear equations is to differentiate the equation to obtain a useful linear equation, and there are various ways for this purpose. We introduce higher-order linearization method so that one can prove the global uniqueness of certain nonlinear equations. Moreover, thanks to the nonlocality, we can also demonstrate a uniqueness result, without using any linearization scheme.