{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:48:40Z","timestamp":1760237320229,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,3,28]],"date-time":"2020-03-28T00:00:00Z","timestamp":1585353600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The Kuramoto\u2013Sinelshchikov\u2013Velarde equation describes the evolution of a phase turbulence in reaction-diffusion systems or the evolution of the plane flame propagation, taking into account the combined influence of diffusion and thermal conduction of the gas on the stability of a plane flame front. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem.<\/jats:p>","DOI":"10.3390\/a13040077","type":"journal-article","created":{"date-parts":[[2020,3,31]],"date-time":"2020-03-31T13:27:19Z","timestamp":1585661239000},"page":"77","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["On Classical Solutions for A Kuramoto\u2013Sinelshchikov\u2013Velarde-Type Equation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6019-4757","authenticated-orcid":false,"given":"Giuseppe Maria","family":"Coclite","sequence":"first","affiliation":[{"name":"Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, 70125 Bari BA, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lorenzo","family":"di Ruvo","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Bari, 70121 Bari BA, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"884","DOI":"10.1137\/0517063","article-title":"The well-posedness of the Kuramoto-Sivashinsky equation","volume":"17","author":"Tadmor","year":"1986","journal-title":"SIAM J. 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