{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:39:09Z","timestamp":1760229549160,"version":"build-2065373602"},"reference-count":10,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T00:00:00Z","timestamp":1655424000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guizhou Provincial Education Foundation of Youth Science and Technology Talent Development","award":["[2016]168","GZMUSK[2021]QN08"],"award-info":[{"award-number":["[2016]168","GZMUSK[2021]QN08"]}]},{"name":"Social Sciences Foundation of Guizhou Minzu University","award":["[2016]168","GZMUSK[2021]QN08"],"award-info":[{"award-number":["[2016]168","GZMUSK[2021]QN08"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The authors of this text study weak solutions to the variational inequalities with degenerate parabolic operators and symmetric structure in Sobolev spaces with variable exponent. The existence and uniqueness of the solutions are treated by using the penalty method and the reduction method in the weak sense. The authors also discuss the nonexistence and long-time behavior of solutions.<\/jats:p>","DOI":"10.3390\/sym14061255","type":"journal-article","created":{"date-parts":[[2022,6,19]],"date-time":"2022-06-19T21:19:26Z","timestamp":1655673566000},"page":"1255","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Study of Weak Solutions for a Class of Degenerate Parabolic Variational Inequalities with Variable Exponent"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6869-1755","authenticated-orcid":false,"given":"Yudong","family":"Sun","sequence":"first","affiliation":[{"name":"School of Political and Economic Management, Guizhou Minzu University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Political and Economic Management, Guizhou Minzu University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/s12044-011-0042-7","article-title":"Overlapping domain decomposition methods for elliptic quasi-variational inequalities related to impulse control problem with mixed boundary conditions","volume":"121","author":"Boulaaras","year":"2011","journal-title":"Proc. Indian Acad. Sci. Math. Sci."},{"key":"ref_2","first-page":"6443","article-title":"L\u221e-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem","volume":"217","author":"Boulaaras","year":"2011","journal-title":"Appl. Math. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.jtusci.2013.05.005","article-title":"The finite element approximation in parabolic quasi-variational inequalities related to impulse control problem with mixed boundary conditions","volume":"7","author":"Boulaaras","year":"2013","journal-title":"J. Taibah Univ. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3063","DOI":"10.1016\/j.jde.2011.07.027","article-title":"American lookback option with fixed strike price 2-D parabolic variational inequality","volume":"251","author":"Chen","year":"2011","journal-title":"J. Differ. 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Inequal. Appl."},{"key":"ref_9","unstructured":"Dibenedetto, E. (2010). Degenerate Parabolic Equations, Springer."},{"key":"ref_10","first-page":"863","article-title":"Existence of solutions to an initial Dirichlet problem of evolutional p(x)-Laplace equations","volume":"29","author":"Lian","year":"2012","journal-title":"Ann. I. H. 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