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Introduction to inverse problems for non-linear partial differential equations

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arxiv 2503.12448 v1 pith:PPWSMLG5 submitted 2025-03-16 math.AP

Matti Lassas This is my paper · ORCID
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keywords problemsequationsinversenon-linearintroductionlinearizationmethodmultiple
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We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is based on self-interaction of linearized waves or other solutions in the presence of non-linearities. Multiple linearization has successfully been used to solve inverse problems for non-linear equation which are still unsolved for the corresponding linear equations.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Affine section tomography for inverse source problems in $k$-Hessian equations with restricted large boundary data

    math.AP 2026-07 accept novelty 7.0 of 10

    Restricted large-data nonlinear DN maps for k-Hessian equations recover a positive source uniquely through the affine q-plane Radon transform of its zero extension.

  2. Gauge rigidity in an inverse problem for the prescribed Gaussian curvature equation

    math.AP 2026-07 accept novelty 6.5 of 10

    If two positive curvatures share the same first boundary jet and induce the same nonlinear DN map on a common open class of admissible boundary data, then the curvatures coincide throughout a planar domain.

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