5 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 L…
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…