Discovery Projects - Grant ID: DP210101102

Funding Activity

Website
http://dataportal.arc.gov.au/NCGP/Web/Grant/Grant/DP210101102

Funding Status
Active

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Funded Activity Summary

Spectral Theory of Hamiltonian Dynamical Systems. Stability theory of steady states, travelling waves, periodic waves, and other coherent structures in nonlinear Hamiltonian partial differential equations is a cornerstone of modern dynamical systems. In particular it is of utmost importance to reliably compute eigenvalues, which determine the stability or instability of such structures. This project will develop methods to compute the spectrum of Hamiltonian operators in more than one spatial dimension. It will use the powerful geometric tools of the Maslov index and the Evans function. We will use these to simultaneously advance, and bring together the theories of the two dimensional Euler equations and Jacobi operators.

Funded Activity Details

Start Date: 01-01-2022

End Date: 31-12-2024

Funding Scheme: Discovery Projects

Funding Amount: $310,000.00

Funder: Australian Research Council

Research Topics

ANZSRC Field of Research (FoR)

Dynamical Systems in Applications | Theoretical and Applied Mechanics | Pure Mathematics | Ordinary Differential Equations, Difference Equations and Dynamical Systems |

ANZSRC Socio-Economic Objective (SEO)

Expanding Knowledge in the Mathematical Sciences

Other Keywords

Dynamical Systems in Applications | Expanding Knowledge in the Mathematical Sciences | Ordinary Differential Equations, Difference Equations and Dynamical Systems | Pure Mathematics | Theoretical and Applied Mechanics

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