8 papers
Carleman--Picard and time-dimensional reduction for inverse initial-data problems in nonlinear transport with memory
Navaraj Neupane, Loc H. Nguyen
We study an inverse initial-data problem for a quasilinear transport equation with nonlinear and memory effects. The unknown initial state is reconstructed from time-dependent meas…
Inverse initial data reconstruction for a memory convection-diffusion equation via Legendre spatial reduction and Tikhonov regularization
Cong B. Van, Thien P. B. Nguyen, Minh-Binh Tran +1
We study an inverse initial data problem for a convection-diffusion equation with memory, where the goal is to recover the unknown initial condition from final-time data. The model…
Forward-Time Black-Scholes Reconstruction via Regularized Legendre Reduction
Phuong M. Nguyen, Matt Nguyen, Loc H. Nguyen
We study a forward-time formulation of the Black-Scholes equation with state-dependent volatility. In contrast to the classical terminal-value pricing problem, where the option pay…
Inverse initial data for nonlinear Schrödinger equation via Carleman estimates and the contraction principle
Navaraj Neupane, Loc Nguyen
We study an inverse initial-data problem for a nonlinear Schrödinger equation in which the initial wave field is reconstructed from lateral measurements. Our approach combines a Le…
Recovery of initial displacement and velocity in anisotropic elastic systems by the time dimensional reduction method
Trong D. Dang, Chanh V. Le, Khoa D. Luu +1
We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields…
A global approach for the inverse scattering problem using a Carleman contraction map
Phuong M. Nguyen, Loc H. Nguyen, Huong T. T. Vu
This paper addresses the inverse scattering problem in the domain Omega. The input data, measured outside Omega, involve the waves generated by the interaction of plane waves with…