Year: 2026
Type: preprint
Abstract: We present a systematic approach to characterize Devaney chaos in the solution of homogeneous one dimensional constant-coefficients PDEs on Herzog spaces. We show that for equations where the highest-order time derivative lacks mixed spatial derivatives, there always exists a weighted space in which the solution is chaotic. This analysis is extended to include mixed partial derivatives in the highest-order temporal term. Moreover, we link the chaotic behavior in Herzog spaces to the semidiscretization of the equations by identifying isometric isomorphisms between the two contexts, providing also a characterization for chaos on these semidiscretizations. The work concludes with two applications that provide new insights on the dynamics of the fourth-order Moore-Gibson-Thompson equation and the viscous van Wijngaarden-Eringen equation.
Source: arXiv (Cornell University)
Author: Vargas-Moreno, Álvaro
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214647830