9 citations · 20 across the 5 of their papers we have counts for
5 papers
Symmetry Groupoids for Pattern-Selective Feedback Stabilization of the Chafee--Infante Equation
Isabelle Schneider, Jia-Yuan Dai
Reaction-diffusion equations are ubiquitous in various scientific domains and their patterns represent a fascinating area of investigation. However, many of these patterns are unst…
Pattern-Selective Feedback Stabilization of Ginzburg--Landau Spiral Waves
Isabelle Schneider, Babette de Wolff, Jia-Yuan Dai
The complex Ginzburg--Landau equation serves as a paradigm of pattern formation and the existence and stability properties of Ginzburg--Landau -armed spiral waves have been inve…
Ginzburg-Landau Spiral Waves in Circular and Spherical Geometries
Jia-Yuan Dai
We prove the existence of -armed spiral wave solutions for the complex Ginzburg-Landau equation in the circular and spherical geometries. We establish a new global bifurcation a…
Ginzburg-Landau patterns in circular and spherical geometries: vortices, spirals and attractors
Jia-Yuan Dai, Phillipo Lappicy
This paper consists of three results on pattern formation of Ginzburg-Landau -armed vortex solutions and spiral waves in circular and spherical geometries. First, we completely…
On the Roots of Characteristic Equations of Delay Differential Systems
Jia-Yuan Dai
We prove that characteristic equations of certain types of delay differential systems, under some mild conditions on their coefficients, can possess infinitely many complex roots.