275 citations · 1.7k across the 132 of their papers we have counts for
149 papers
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…
Introduction to inverse problems for non-linear partial differential equations
Matti Lassas
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of…
Stroke classification using Virtual Hybrid Edge Detection from in silico electrical impedance tomography data
Juan Pablo Agnelli, Fernando S. Moura, Siiri Rautio +4
Electrical impedance tomography (EIT) is a non-invasive imaging method for recovering the internal conductivity of a physical body from electric boundary measurements. EIT combined…
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…