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PreprintCC BY 4.0arXiv

A Systematic Approach to Chaos In PDEs and their Semidiscretizations

  • Álvaro Vargas-Moreno
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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.

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Cite

BibTeXRIS
BibTeX
@misc{vargasmoreno2026systematic,
  title = {{A Systematic Approach to Chaos In PDEs and their Semidiscretizations}},
  author = {Álvaro Vargas-Moreno},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31126},
  eprint = {2609.31126},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31126},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Systematic Approach to Chaos In PDEs and their Semidiscretizations
AU  - Álvaro Vargas-Moreno
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.31126
UR  - https://arxiv.org/abs/2609.31126
AB  - 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.
ER  -