14 citations · 32 across the 12 of their papers we have counts for
15 papers
Optimal stability of regularized spectral differentiation in Sobolev spaces
Teemu Tyni
We study the problem of stable spectral differentiation of functions in Sobolev spaces from noisy data. We introduce a class of admissible Fourier multipliers under simple and dire…
Reconstruction for an inverse scattering problem with a Kerr type nonlinearity
Khaoula El Maddah, Matti Lassas, Tony Liimatainen +2
We study the inverse scattering problem for the Kerr-nonlinear Helmholtz equation \[ Δu + k^2(1+q(x)|u|^2)u = 0 \quad \text{in }\mathbb{R}^n,\; n\geq 2, \] where the aim is to reco…
Numerical reconstruction of Schrödinger equations with quadratic nonlinearities
Khaoula El Maddah, Matti Lassas, Teemu Tyni
We introduce a numerical framework for reconstructing the potential in two dimensional semilinear elliptic PDEs with power type nonlinearities from the nonlinear Dirichlet to Neuma…
Gaussian beam interactions and inverse source problems for nonlinear wave equations
Matti Lassas, Tony Liimatainen, Valter Pohjola +1
We study the inverse source problem for the semilinear wave equation \[ (\Box_g + q_1)u + q_2 u^2 = F, \] on a globally hyperbolic Lorentzian manifold. We demonstrate that the coef…
X-ray imaging from nonlinear waves: numerical reconstruction of a cubic nonlinearity
Suvi Anttila, Markus Harju, Teemu Tyni
We study an inverse boundary value problem for the nonlinear wave equation in dimensions. The objective is to recover an unknown potential from the associated Dir…
Inverse scattering problems for non-linear wave equations on Lorentzian manifolds
Spyros Alexakis, Hiroshi Isozaki, Matti Lassas +1
We show that an inverse scattering problem for a semilinear wave equation can be solved on a manifold having an asymptotically Minkowskian infinity, that is, scattering functionals…
Optimal Runge approximation for nonlocal wave equations and unique determination of polyhomogeneous nonlinearities
Yi-Hsuan Lin, Teemu Tyni, Philipp Zimmermann
The main purpose of this article is to establish the Runge-type approximation in for solutions of linear nonlocal wave equations. To achieve this, we…
Well-posedness and inverse problems for semilinear nonlocal wave equations
Yi-Hsuan Lin, Teemu Tyni, Philipp Zimmermann
This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results…
A boundary integral equation method for the complete electrode model in electrical impedance tomography with tests on experimental data
Teemu Tyni, Adam R Stinchcombe, Spyros Alexakis
We develop a boundary integral equation-based numerical method to solve for the electrostatic potential in two dimensions, inside a medium with piecewise constant conductivity, whe…
Stability estimates for the inverse fractional conductivity problem
Giovanni Covi, Jesse Railo, Teemu Tyni +1
We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem…
An inverse problem for a semi-linear wave equation: a numerical study
Matti Lassas, Tony Liimatainen, Leyter Potenciano-Machado +1
We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in dimensions. We develop a numerical schem…
Stability estimates for inverse problems for semi-linear wave equations on Lorentzian manifolds
Matti Lassas, Tony Liimatainen, Leyter Potenciano-Machado +1
This paper concerns an inverse boundary value problem of recovering a zeroth order time-dependent term of a semi-linear wave equation on a globally hyperbolic Lorentzian manifold.…
Inverse problems for elliptic equations with fractional power type nonlinearities
Tony Liimatainen, Yi-Hsuan Lin, Mikko Salo +1
We study inverse problems for semilinear elliptic equations with fractional power type nonlinearities. Our arguments are based on the higher order linearization method, which helps…
Uniqueness and stability of an inverse problem for a semi-linear wave equation
Matti Lassas, Tony Liimatainen, Leyter Potenciano-Machado +1
We consider the recovery of a potential associated with a semi-linear wave equation on , . We show a Hölder stability estimate for the recovery of an unk…
Optimal recovery of a radiating source with multiple frequencies along one line
Tommi Brander, Joonas Ilmavirta, Petteri Piiroinen +1
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is moti…