9 papers
Spectral Algorithms for 3-Wave Kinetic and Quantum Boltzmann Equations with General Resonance Manifolds in
Thanh Trung Le, Minh-Binh Tran
Following recent developments in numerical schemes for 3-wave kinetic equations [2, 7, 42, 44, 43], we develop spectral algorithms for multidimensional 3-wave kinetic equations and…
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…
On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas
Peter S. Madsen, Phan Thành Nam, Herbert Spohn +1
This paper is devoted to the dynamics of a weakly interacting Fermi gas at the kinetic time regime where is the strength of the interaction potential. We pr…
Entropy Structures and Long-Time Relaxation for 3-Wave Kinetic Equations
Gigliola Staffilani, Minh-Binh Tran
We establish a new class of entropy structures for \(3\)-wave kinetic equations with a broad family of interaction weights. Unlike the classical entropies arising from detailed bal…
A globally convergent Carleman-Picard method for an inverse initial-value problem for a nonlinear diffusive coagulation-fragmentation equation coagulation-fragmentation equation
Thuy T. Le, Minh-Binh Tran, Loc H. Nguyen
We study an inverse initial-density problem for a nonlinear diffusive coagulation--fragmentation equation with known coagulation and fragmentation kernels. The objective is to reco…
Analysis of a numerical scheme for 3-wave kinetic equations
Minh-Binh Tran, Bangjie Wang
Several numerical schemes for 3-wave kinetic equations have been proposed in recent work and shown to be accurate and computationally efficient [8,33,34,35]. However, their rigorou…
An energy cascade finite volume scheme for a mixed 3- and 4-wave kinetic equation arising from the theory of finite-temperature trapped Bose gases
Arijit Das, Minh-Binh Tran
Building on recent developments in numerical schemes designed to capture energy cascades for 3-wave kinetic equations~\cite{das2024numerical, walton2022deep, walton2023numerical, w…
Numerical schemes for a fully nonlinear coagulation-fragmentation model coming from wave kinetic theory
Arijit Das, Minh-Binh Tran
This article introduces a novel numerical approach, based on Finite Volume Techniques, for studying fully nonlinear coagulation-fragmentation models, where both the coagulation and…
Numerical Schemes for 3-Wave Kinetic Equations: A Complete Treatment of the Collision Operator
Steven Walton, Minh-Binh Tran
In our previous work, numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, ha…