3 papers
math.DS2023
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…
math.AP2020
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…
math.DS2016
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.