GLOBAL WAVEFRONT PROPAGATION AND NON-ELLIPTIC FREDHOLM THEORY

Grant number: DP180100589 | Funding period: 2018 - 2022

Completed

Abstract

Many significant phenomena in the natural world are described by partial differential equations that involve evolution in time. This project aims to develop new mathematical methods, involving recently discovered global wavefront set analysis and Fredholm theory, to solve such equations. These methods aim to extend the range of equations that can be solved as well as yield more information about solutions, in particular, their long-time asymptotics.

Related publications (2)

EXISTENCE AND ASYMPTOTICS OF NONLINEAR HELMHOLTZ EIGENFUNCTIONS

Jesse Gell-Redman, Andrew Hassell, Jacob Shapiro, Junyong Zhang

2020-01-01

We prove the existence and asymptotic expansion of a large class of solutions to nonlinear Helmholtz equations of the form (Δ-λ2)u..

Equidistribution of phase shifts in obstacle scattering

Jesse Gell-Redman, Maxime Ingremeau

2019-01-02

For scattering off a smooth, strictly convex obstacle (Formula presented.) with positive curvature, we show that the eigenvalues o..

University of Melbourne Researchers

Jesse Gell-Redman Mathematics and Statistics