6 papers
Fourier--Laplace Injectivity for Oblique and Polygonal Cylinders in Passive Inverse Problems
Yan Jiang, Hongyu Liu, Tianhao Ni +1
We study Fourier--Laplace transforms on null phases arising in passive inverse problems. Densities with codimension-one dependence in oblique cylinders are first considered. Integr…
DTPFI: A stable algorithm for recovering nonlinear energy potentials in phase field systems
Tianhao Ni, Jun Lai
This work proposes a Dual Time Phase Field Inversion (DTPFI) method for recovering unknown potential functions in phase field models. The reconstruction is formulated as an optimiz…
Inverse problems for a quasilinear hyperbolic equation with multiple unknowns
Yan Jiang, Hongyu Liu, Tianhao Ni +1
We propose and study several inverse boundary problems associated with a quasilinear hyperbolic equation of the form on a compact…
A uniqueness theory on determining the nonlinear energy potential in phase-field system
Tianhao Ni, Jun Lai
The phase-field system is a nonlinear model that has significant applications in material sciences. In this paper, we are concerned with the uniqueness of determining the nonlinear…
Inverse problems for nonlinear progressive waves
Yan Jiang, Hongyu Liu, Tianhao Ni +1
We propose and study several inverse problems associated with the nonlinear progressive waves that arise in infrasonic inversions. The nonlinear progressive equation (NPE) is of a…
A Modified Nonlinear Conjugate Gradient Algorithm for Functions with Non-Lipschitz Gradient
Bingjie Li, Tianhao Ni, Zhenyue Zhang
In this paper, we propose a modified nonlinear conjugate gradient (NCG) method for functions with a non-Lipschitz continuous gradient. First, we present a new formula for the conju…