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Article Dans Une Revue Journal of the London Mathematical Society Année : 2021

On the determination of nonlinear terms appearing in semilinear hyperbolic equations

Résumé

We consider the inverse problem of determining a general nonlinear term appearing in a semilin-ear hyperbolic equation on a Riemannian manifold with boundary (M, g) of dimension n = 2, 3. We prove results of unique recovery of the nonlinear term F (t, x, u), appearing in the equation ∂ 2 t u−∆gu+F (t, x, u) = 0 on (0, T) × M with T > 0, from some partial knowledge of the solutions u on the boundary of the time-space cylindrical manifold (0, T) × M or on the lateral boundary (0, T) × ∂M. We determine the expression F (t, x, u) both on the boundary x ∈ ∂M and inside the manifold x ∈ M .
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Dates et versions

hal-01830728 , version 1 (05-07-2018)

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Yavar Kian. On the determination of nonlinear terms appearing in semilinear hyperbolic equations. Journal of the London Mathematical Society, 2021, 104 (2), pp.572-595. ⟨10.1112/jlms.12440⟩. ⟨hal-01830728⟩
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