https://scholars.lib.ntu.edu.tw/handle/123456789/638948
Title: | Inverse problems for some fractional equations with general nonlinearity | Authors: | Kow, Pu Zhao JENN-NAN WANG |
Keywords: | Fractional Laplacian | Global uniqueness of inverse problems | Hartree potentials | Kerr-type nonlinearity | Nonlinear potentials | Issue Date: | 1-Dec-2023 | Journal Volume: | 10 | Journal Issue: | 4 | Source: | Research in Mathematical Sciences | Abstract: | Inspired by some interesting equations modeling anomalous diffusion and nonlinear phenomena, we will study the inverse problems of uniquely identifying coefficients in nonlinear terms from over-determined data. Precisely, we consider a semilinear fractional Schrödinger operator (- Δ) su+ Q(x, u) = 0 in Ω with 0 < s< 1 . The fractional Laplacian arises due to the anomalous diffusion, e.g., the motion of particles described by Lévy flights. Here, we consider the semilinear term Q(x, u) = q(x, | u|) u , which appears naturally in the study of nonlinear optics with cubic Kerr-type nonlinearity, the complex Ginzburg–Landau equation with cubic-quintic nonlinearity, or even the Hartree equation with convolution-type nonlinearity, etc. In this article, we consider the time-independent and the time-evolution semilinear fractional Schrödinger equations with “Dirichlet” condition given on the complement of Ω . We prove both the well-posedness of the forward problems and the unique determination of the inverse problems with measurements taken on the complement of Ω . |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/638948 | ISSN: | 25220144 | DOI: | 10.1007/s40687-023-00409-8 |
Appears in Collections: | 應用數學科學研究所 |
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