9 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 \[ Îu + k^2(1+q(x)|u|^2)u = 0 \quad \text{in }\mathbb{R}^n,\; n\geq 2, \] where the aim is to rec…
An inverse problem for fractional random walks on finite graphs
Giovanni Covi, Matti Lassas
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity γ is defined. Our data consists in a sequence of partial observations of a fra…
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…
Reconstruction of anisotropic stiffness tensors from partial data around one polarization
Maarten V. de Hoop, Joonas Ilmavirta, Matti Lassas +1
We study inverse problems in anisotropic elasticity using tools from algebraic geometry. The singularities of solutions to the elastic wave equation in dimension with an anisot…
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…