1 citations · 1 across the 5 of their papers we have counts for
5 papers
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…
Speed of propagation of fractional dispersive waves
Brian Choi, Steven Walton
In this paper, we show that all non-trivial solutions of a broad class of nonlinear dispersive equations, whose linear evolution is governed by a dispersion relation under minimal…
A Deep Learning Approximation of Non-Stationary Solutions to Wave Kinetic Equations
Steven Walton, Minh-Binh Tran, Alain Bensoussan
We present a deep learning approximation, stochastic optimization based, method for wave kinetic equations. To build confidence in our approach, we apply the method to a Smoluchows…
Null-Controllability of a Non-Local Heat Equation
Steven Walton
We consider the null-controllability of a non-local heat equation by interior controls. We confirm a conjecture of Lissy and Zuazua by showing that it is enough to assume…
A Numerical Scheme for Wave Turbulence: 3-Wave Kinetic Equations
Steven Walton, Minh-Binh Tran
We introduce a finite volume scheme to solve a special case of isotropic 3-wave kinetic equations. We test our numerical solution against theoretical results concerning the long ti…