Zobrazeno 1 - 10
of 46
pro vyhledávání: '"Lizarraga, Ian"'
Reaction-nonlinear diffusion (RND) partial differential equations are a fruitful playground to model the formation of sharp travelling fronts, a fundamental pattern in nature. In this work, we demonstrate the utility and scope of regularisation as a
Externí odkaz:
http://arxiv.org/abs/2308.02719
Autor:
Lizarraga, Ian, Marangell, Robert
We determine the nonlinear stability of shock-fronted travelling waves arising in a reaction-nonlinear diffusion PDE, subject to a fourth-order spatial derivative term multiplied by a small parameter $\varepsilon$ that models {\it nonlocal regulariza
Externí odkaz:
http://arxiv.org/abs/2211.07824
Autor:
Lizarraga, Ian, Marangell, Robert
Reaction-nonlinear diffusion partial differential equations can exhibit shock-fronted travelling wave solutions. Prior work by Yi et. al. (2021) has demonstrated the existence of such waves for two classes of regularisations, including viscous relaxa
Externí odkaz:
http://arxiv.org/abs/2208.10064
Autor:
Lizarraga, Ian, Marangell, Robert
Publikováno v:
In Physica D: Nonlinear Phenomena April 2024 460
We present a novel method for computing slow manifolds and their fast fibre bundles in geometric singular perturbation problems. This coordinate-independent method is inspired by the parametrisation method introduced by Cabr\'e, Fontich and de la Lla
Externí odkaz:
http://arxiv.org/abs/2009.10583
We develop the contact singularity theory for singularly-perturbed (or `slow-fast') vector fields of the general form $z' = H(z,\varepsilon)$, $z\in\mathbb{R}^n$ and $\varepsilon\ll 1$. Our main result is the derivation of computable, coordinate-inde
Externí odkaz:
http://arxiv.org/abs/2004.01825
Autor:
Lizarraga, Ian, Wechselberger, Martin
The computational singular perturbation (CSP) method is an algorithm which iteratively approximates slow manifolds and fast fibers in multiple-timescale dynamical systems. Since its inception due to Lam and Goussis, the convergence of the CSP method
Externí odkaz:
http://arxiv.org/abs/1906.06049
Autor:
Lizarraga, Ian1 (AUTHOR) ian.lizarraga@sydney.edu.au, Marangell, Robert1 (AUTHOR)
Publikováno v:
Journal of Nonlinear Science. Oct2023, Vol. 33 Issue 5, p1-71. 71p.
Autor:
Bradshaw-Hajek, Bronwyn H.1 bronwyn.hajek@unisa.edu.au, Lizarraga, Ian2 ian.lizarraga@sydney.edu.au, Marangell, Robert2 robert.marangell@sydney.edu.au, Wechselberger, Martin2 martin.wechselberger@sydney.edu.au
Publikováno v:
SIAM Journal on Applied Dynamical Systems. 2024, Vol. 23 Issue 3, p2099-2137. 39p.
Autor:
Lizarraga, Ian
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic orbit emergin
Externí odkaz:
http://arxiv.org/abs/1512.04641