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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:p> Many physical systems are represented by Partial Differential Equations (PDEs), and the study of chaotic dynamics in these systems is interesting and challenging. In this paper, the Li\u2013Yorke chaos of PDEs is studied, and the Li\u2013Yorke chaos is observable in several classes of PDEs, including systems with or without energy injection. For the PDEs without energy injection, three kinds of PDEs are investigated revealing the existence of Li\u2013Yorke chaos, including a type of transport equations, a class of wave equations, and a kind of Navier\u2013Stokes equations. For the PDEs with energy injection, only dissipative type of PDEs are studied, including a model of sound variation of the drum with damping, a kind of reaction\u2013diffusion equations, and a class of two-dimensional Navier\u2013Stokes equations. It is shown that Li\u2013Yorke chaos is well defined for the characterization of the complicated dynamics of these systems. In particular, a physical explanation about chaos in such PDEs is provided, which gives an interesting explanation of acoustic chaos. <\/jats:p>","DOI":"10.1142\/s0218127425500245","type":"journal-article","created":{"date-parts":[[2025,1,30]],"date-time":"2025-01-30T02:35:51Z","timestamp":1738204551000},"source":"Crossref","is-referenced-by-count":2,"title":["Li\u2013Yorke Chaos in Partial Differential Equations with or Without Energy Injection"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5138-6631","authenticated-orcid":false,"given":"Xu","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shandong University, Weihai 264209, Shandong, P. R. 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