52 citations · 103 across the 12 of their papers we have counts for
14 papers
A Proximal Primal-Dual Approach to Generalized JKO Schemes for Doubly Nonlinear Parabolic Equations
Luis M. Briceño-Arias, José A. Carrillo, Dante Kalise +2
Variational methods based on optimization strategies are proposed to numerically solve a large family of nonlinear partial differential equations. They are all particular instances…
Perturbation Function Iteration Method: A New Framework for Solving Periodic Solutions of Non-linear and Non-smooth Systems
Limin Cao, Yanmao Chen, Li Wang +2
Computing accurate periodic responses in strongly nonlinear or even non-smooth vibration systems remains a fundamental challenge in nonlinear dynamics. Existing numerical methods,…
The Evolution of Pointwise Statistics in Hyperbolic Equations with Random Data
Alina Chertock, Pierre Degond, Amir Sagiv +1
We consider one-dimensional hyperbolic PDEs, linear and nonlinear, with random initial data. Our focus is the {\em pointwise statistics,} i.e., the probability measure of the solut…
To blow-up or not to blow-up for a granular kinetic equation
José A. Carrillo, Ruiwen Shu, Li Wang +1
A simplified kinetic description of rapid granular media leads to a nonlocal Vlasov-type equation with a convolution integral operator that is of the same form as the continuity eq…
Structure preserving primal dual methods for gradient flows with nonlinear mobility transport distances
Jose A. Carrillo, Li Wang, Chaozhen Wei
We develop structure preserving schemes for a class of nonlinear mobility continuity equation. When the mobility is a concave function, this equation admits a form of gradient flow…
Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations
Wuzhe Xu, Yulong Lu, Li Wang
Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations. In particular, i…