On the determination of nonlinear terms appearing in semilinear hyperbolic equations

Abstract : 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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Submitted on : Thursday, July 5, 2018 - 12:34:49 PM
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Yavar Kian. On the determination of nonlinear terms appearing in semilinear hyperbolic equations. 2018. ⟨hal-01830728⟩

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