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Recovery of a cubic non-linearity in the wave equation in the weakly non-linear regime
We study the inverse problem of recovery a compactly supported non-linearity in the
semilinear wave equation u tt-Δ u+ α (x)| u| 2 u= 0, in two and three dimensions. We probe …
semilinear wave equation u tt-Δ u+ α (x)| u| 2 u= 0, in two and three dimensions. We probe …
An inverse boundary value problem for a semilinear wave equation on Lorentzian manifolds
We consider an inverse boundary value problem for a semilinear wave equation on a time-
dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of …
dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of …
The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds
We consider the semilinear wave equation□ gu+ au 4= 0, a≠ 0, on a Lorentzian manifold
(M, g) with timelike boundary. We show that from the knowledge of the Dirichlet-to-Neumann …
(M, g) with timelike boundary. We show that from the knowledge of the Dirichlet-to-Neumann …
[PDF][PDF] Inverse problems for nonlinear hyperbolic equations.
There has been considerable progress in recent years in solving inverse problems for
nonlinear hyperbolic equations. One of the striking aspects of these developments is the use …
nonlinear hyperbolic equations. One of the striking aspects of these developments is the use …
An inverse boundary value problem arising in nonlinear acoustics
We consider an inverse problem arising in nonlinear ultrasound imaging. The propagation
of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at …
of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at …
Scattering rigidity for standard stationary manifolds via timelike geodesics
S Muñoz-Thon - arxiv preprint arxiv:2404.09449, 2024 - arxiv.org
We study the scattering rigidity problem for standard stationary manifolds using timelike
geodesics with a fixed momentum. Taking advantage of the symmetry of this manifolds, we …
geodesics with a fixed momentum. Taking advantage of the symmetry of this manifolds, we …
Recovery of a general nonlinearity in the semilinear wave equation
We study the inverse problem of recovery a nonlinearity f (t, x, u), which is compactly
supported in x, in the semilinear wave equation u tt− Δ u+ f (t, x, u)= 0. We probe the medium …
supported in x, in the semilinear wave equation u tt− Δ u+ f (t, x, u)= 0. We probe the medium …
Inverse problem for the Yang–Mills equations
We show that a connection can be recovered up to gauge from source-to-solution type data
associated with the Yang–Mills equations in Minkowski space R^ 1+ 3 R 1+ 3. Our proof …
associated with the Yang–Mills equations in Minkowski space R^ 1+ 3 R 1+ 3. Our proof …
Inverse problem for Einstein-scalar field equations
The paper introduces a method to solve inverse problems for hyperbolic systems where the
leading-order terms are nonlinear. We apply the method to the coupled Einstein-scalar field …
leading-order terms are nonlinear. We apply the method to the coupled Einstein-scalar field …
Weakly nonlinear geometric optics for the Westervelt equation and recovery of the nonlinearity
We study the nondiffusive Westervelt equation in the weakly nonlinear regime and show that
the leading profile equation is of Burgers' type. We show that a compactly supported …
the leading profile equation is of Burgers' type. We show that a compactly supported …