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[HTML][HTML] Uniqueness, reconstruction and stability for an inverse problem of a semi-linear wave equation
We consider the recovery of a potential associated with a semi-linear wave equation on R
n+ 1, n≥ 1. We show that an unknown potential a (x, t) of the wave equation□ u+ aum= 0 …
n+ 1, n≥ 1. We show that an unknown potential a (x, t) of the wave equation□ u+ aum= 0 …
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 …
Nonlinear ultrasound imaging modeled by a Westervelt equation
We consider the ultrasound imaging problem governed by a nonlinear wave equation of
Westervelt type with variable wave speed. We show that the coefficient of nonlinearity can …
Westervelt type with variable wave speed. We show that the coefficient of nonlinearity can …
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 …
An inverse problem for a semilinear elliptic equation on conformally transversally anisotropic manifolds
Given a conformally transversally anisotropic manifold (M, g), we consider the semilinear
elliptic equation (-Δ g+ V) u+ qu 2= 0 on M. We show that an a priori unknown smooth …
elliptic equation (-Δ g+ V) u+ qu 2= 0 on M. We show that an a priori unknown smooth …
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 …
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 …
An inverse problem for the wave equation with nonlinear dum**
VG Romanov - Siberian Mathematical Journal, 2023 - Springer
We study the inverse problem of recovering a coefficient at the nonlinearity in a second
order hyperbolic equation with nonlinear dam**. The unknown coefficient depends on …
order hyperbolic equation with nonlinear dam**. The unknown coefficient depends on …
Inverse boundary value problems for wave equations with quadratic nonlinearities
We study inverse problems for the nonlinear wave equation□ g u+ w (x, u,∇ gu)= 0 in a
Lorentzian manifold (M, g) with boundary, where∇ gu denotes the gradient and w (x, u, ξ) is …
Lorentzian manifold (M, g) with boundary, where∇ gu denotes the gradient and w (x, u, ξ) is …
Nonlinear acoustic imaging with dam**
Y Zhang - ar**
term and a general nonlinear term. This problem arises in nonlinear acoustic imaging and …
term and a general nonlinear term. This problem arises in nonlinear acoustic imaging and …