Abstract: To stabilize partial differential equation (PDE) models, control laws typically require space-dependent functional gains mapped by nonlinear operators from the PDE functional coefficients.

ABSTRACT: This paper is concerned with a modified transitional Korteweg-de Vries equation u t +f( t ) u 2 u x + u xxx =0 , ( x,t )∈ R + × R + with initial value u( x,0 )=g( x )∈ H 4 ( R + ) and ...

The data and code for the paper One-shot learning for solution operators of partial differential equations. arXiv preprint arXiv:2104.05512, 2021. The code for training the local solution operators, ...

Fokker-Planck PDEs (including diffusions) for stable Lévy processes (including Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image ...