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arXiv · 2506.19447

An inverse problem for semilinear elliptic equations with generalized Kerr-type nonlinearities

Pu-Zhao Kow·Rulin Kuan
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Abstract

We study the inverse problem of reconstructing the convex hull of unknown inclusions in semilinear elliptic equations with nonanalytic nonlinearities, by extending Ikehata's enclosure method to accommodate such nonlinear effects. To overcome the lack of the higher-order differentiability required for the Taylor-based construction, we construct an approximate solution based on the linearized equation through a first-iteration approximation. Under suitable structural conditions on the nonlinearity, we establish a reconstruction result for the convex hull of the inclusion. The method applies to a broad class of generalized Kerr-type nonlinearities that need not be analytic, without requiring an explicit formula for the nonlinear term.

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Pu-Zhao Kow, Rulin Kuan. 2026-09-17. An inverse problem for semilinear elliptic equations with generalized Kerr-type nonlinearities. https://arxiv.org/abs/2506.19447

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