Recovery of a cubic non-linearity in the wave equation in the weakly non-linear regime

A Sá Barreto, P Stefanov - Communications in Mathematical Physics, 2022‏ - Springer
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 …

An inverse boundary value problem for a semilinear wave equation on Lorentzian manifolds

P Hintz, G Uhlmann, J Zhai - … Mathematics Research Notices, 2022‏ - academic.oup.com
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 …

The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds

P Hintz, G Uhlmann, J Zhai - Communications in Partial Differential …, 2022‏ - Taylor & Francis
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 …

[PDF][PDF] Inverse problems for nonlinear hyperbolic equations.

G Uhlmann, J Zhai - … & Continuous Dynamical Systems: Series A, 2021‏ - researchgate.net
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 …

An inverse boundary value problem arising in nonlinear acoustics

G Uhlmann, Y Zhang - SIAM Journal on Mathematical Analysis, 2023‏ - SIAM
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 …

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 …

Recovery of a general nonlinearity in the semilinear wave equation

A Sá Barreto, P Stefanov - Asymptotic Analysis, 2024‏ - journals.sagepub.com
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 …

Inverse problem for the Yang–Mills equations

X Chen, M Lassas, L Oksanen… - … in Mathematical Physics, 2021‏ - Springer
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 …

Inverse problem for Einstein-scalar field equations

Y Kurylev, M Lassas, L Oksanen… - Duke Mathematical …, 2022‏ - projecteuclid.org
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 …

Weakly nonlinear geometric optics for the Westervelt equation and recovery of the nonlinearity

N Eptaminitakis, P Stefanov - SIAM Journal on Mathematical Analysis, 2024‏ - SIAM
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 …