{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:37:11Z","timestamp":1760402231471,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,4]],"date-time":"2022-01-04T00:00:00Z","timestamp":1641254400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We study the structural stability for the double-diffusion perturbation equations. Using the a priori bounds, the convergence results on the reaction boundary coefficients k1, k2 and the Lewis coefficient Le could be obtained with the aid of some Poincare\u00b4 inequalities. The results showed that the structural stability is valid for the the double-diffusion perturbation equations with reaction boundary conditions. Our results can be seen as a version of symmetry in inequality for studying the structural stability.<\/jats:p>","DOI":"10.3390\/sym14010067","type":"journal-article","created":{"date-parts":[[2022,1,9]],"date-time":"2022-01-09T23:35:09Z","timestamp":1641771309000},"page":"67","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Convergence Results for the Double-Diffusion Perturbation Equations"],"prefix":"10.3390","volume":"14","author":[{"given":"Jincheng","family":"Shi","sequence":"first","affiliation":[{"name":"School of Data Science, Guangzhou Huashang College, Guangzhou 511300, China"}]},{"given":"Shiguang","family":"Luo","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Guangdong University of Finance, Guangzhou 510521, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ames, K.A., and Straughan, B. 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