论文标题
大型$ | k | $复杂的几何光学解决方案d-bar问题的行为
Large $|k|$ behavior of complex geometric optics solutions to d-bar problems
论文作者
论文摘要
对于频谱参数$ k $的庞大值，研究了在电阻抗中出现的D-BAR方程系统的复杂几何光学解决方案。对于潜力\（q \ in \ langle \ cdot \ rangle^{ - 2} h^{s}（\ mathbb {c}）\ in] 1,2] $的某些$ s \）\ in，它表明该解决方案作为$ 1/| k | k | k |^s-1} $ nose conlesge converge conlesge converge converge converge conlesge converge converge converge converge converge converge conseges。对于潜在的$ q $，是具有光滑边界的严格凸出设置的特征功能，它仍然具有$ s = 3/2 $，即带有$ 1/\ sqrt {| k |} $而不是$ 1/| k | |^{s-1} $。明确计算领先的顺序概念。数值模拟显示了渐近公式在磁盘特征函数示例中的适用性。
Complex geometric optics solutions to a system of d-bar equations appearing in the context of electrical impedance tomography and the scattering theory of the integrable Davey-Stewartson II equations are studied for large values of the spectral parameter $k$. For potentials \( q\in \langle \cdot \rangle^{-2} H^{s}(\mathbb{C}) \) for some $s \in]1,2]$, it is shown that the solution converges as the geometric series in $1/|k|^{s-1}$. For potentials $q$ being the characteristic function of a strictly convex open set with smooth boundary, this still holds with $s=3/2$ i.e., with $1/\sqrt{|k|}$ instead of $1/|k|^{s-1}$. The leading order controbutions are computed explicitly. Numerical simulations show the applicability of the asymptotic formulae for the example of the characteristic function of the disk.
