5 papers
Reconstruction of shear modulus inclusions in elastostatics via divergence-free localization
Henrik Garde, Nuutti Hyvönen, Valter Pohjola
We formulate an improved version of the monotonicity method for shape reconstruction in the inverse problem of linear elastostatics. We show that this method can reconstruct inclus…
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…
On the growth properties of interior transmission eigenfunctions near corners
Emilia L. K. Blåsten, Valter Pohjola
We investigate the localization and vanishing of interior transmission eigenfunctions at corners. Past numerical computations suggest that these eigenfunctions localize at no…
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…
The linearized monotonicity method for elastic waves and the separation of material parameters
Sarah Eberle-Blick, Valter Pohjola
We derive a linearized version of the monotonicity method for shape reconstruction using time harmonic elastic waves. The linearized method provides an efficient version of the met…