7 papers
Determination of hyperelastic parameters with non-trapping wavespeeds
Gunther Uhlmann, Jian Zhai
We consider the elastic wave equation in three-dimensional isotropic medium with up to quadratic nonlinear terms. We show that five out of the six elastic parameters can be uniquel…
Determination of an anisotropic perturbation in elastic inverse scattering
Matti Lassas, Shiqi Ma, Lauri Oksanen +2
We consider a linearized inverse scattering problem for elastic waves. We prove that a fully anisotropic perturbation of the elastic parameters around an isotropic and homogeneous…
An inverse problem for compressible Euler's equations
Gunther Uhlmann, Yuchao Yi, Jian Zhai
We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine t…
An inverse problem in optimal transport on closed Riemannian manifolds
Jian Zhai, Kelvin Shuangjian Zhang
We consider the problem of recovering the Riemannian metric on a compact closed manifold from the optimal transport maps when the underlying cost function is the squared Riemann di…
On the anisotropic Calderón's problem
Gunther Uhlmann, Jian Zhai
We prove that the Riemannian metric on a compact manifold of dimension with smooth boundary can be uniquely determined, up to an isometry fixing the boundary, by the Diri…
Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors
Gunther Uhlmann, Jian Zhai
Consider a compact Riemannian manifold in dimension with strictly convex boundary. We show the local invertibility near a boundary point of the transverse ray transform of …
Invertibility of local geodesic transverse and mixed ray transforms I: basic cases
Gunther Uhlmann, Jian Zhai
Consider a compact Riemannian manifold in dimension with strictly convex boundary. We show that the transverse ray transform of tensors and the mixed ray transform of…