Well-posedness of the Goursat problem and stability for point source inverse backscattering
Well-posedness of the Goursat problem and stability for point source inverse backscattering
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Goursat 问题的适定性和点源逆后向散射的稳定性
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发表时间：
2017
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通讯作者：
E. Blaasten
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作者：
E. Blaasten
在角度控制势的假设下，证明了点源逆后向散射问题的对数稳定性。径向对称意味着Hölder稳定性。重要的是，我们还证明了点源方程是适定的，并且相关的特征初值问题或Goursat问题也是适定的。这些后一种结果在文献中很难以稳定性证明所要求的形式找到。MSC课程：35R30、78A46、35A08、35L15
We show logarithmic stability for the point source inverse backscattering problem under the assumption of angularly controlled potentials. Radial symmetry implies Hölder stability. Importantly, we also show that the point source equation is well-posed and also that the associated characteristic initial value problem, or Goursat problem, is well-posed. These latter results are difficult to find in the literature in the form required by the stability proof. MSC classes: 35R30, 78A46, 35A08, 35L15