{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:08:11Z","timestamp":1740103691882,"version":"3.37.3"},"reference-count":42,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T00:00:00Z","timestamp":1584316800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11701465)"],"award-info":[{"award-number":["11701465)"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,3,16]]},"abstract":"<jats:p>This paper is concerned with a nonlinear viscoelastic Kirchhoff plate <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>t<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mo>\u2212<\/mml:mo><mml:mi>\u03c3<\/mml:mi><mml:mi>\u0394<\/mml:mi><mml:msub><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>t<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mo>+<\/mml:mo><mml:msup><mml:mrow><mml:mi>\u0394<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mi>u<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mo>\u2212<\/mml:mo><mml:mstyle displaystyle=\"true\"><mml:mrow><mml:msubsup><mml:mo stretchy=\"false\">\u222b<\/mml:mo><mml:mn>0<\/mml:mn><mml:mi>t<\/mml:mi><\/mml:msubsup><mml:mrow><mml:mi>g<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>t<\/mml:mi><mml:mo>\u2212<\/mml:mo><mml:mi>s<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:msup><mml:mrow><mml:mi>\u0394<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mi>u<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>s<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mtext>d<\/mml:mtext><mml:mi>s<\/mml:mi><\/mml:mrow><\/mml:mrow><\/mml:mstyle><mml:mo>=<\/mml:mo><mml:mtext>div<\/mml:mtext><mml:mi>F<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mo>\u2207<\/mml:mo><mml:mi>u<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mfenced><mml:mo>.<\/mml:mo><\/mml:mrow><\/mml:math> By assuming the minimal conditions on the relaxation function <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>g<\/mml:mi><\/mml:math>: <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msup><mml:mrow><mml:mi>g<\/mml:mi><\/mml:mrow><mml:mrow><mml:mo>\u2032<\/mml:mo><\/mml:mrow><\/mml:msup><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mo>\u2264<\/mml:mo><mml:mi>\u03be<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mi>G<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>g<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math>, where <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mi>G<\/mml:mi><\/mml:math> is a convex function, we establish optimal explicit and general energy decay results to the system. Our result holds for <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>G<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:mfenced><mml:mo>=<\/mml:mo><mml:mi>t<\/mml:mi><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math> with the range <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>p<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mfenced open=\"[\" close=\")\" separators=\"|\"><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><mml:mtext>\u2009<\/mml:mtext><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math>, which improves earlier decay results with the range <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi>p<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mfenced open=\"[\" close=\")\" separators=\"|\"><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><mml:mrow><mml:mn>3<\/mml:mn><mml:mo>\/<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math>. At last, we give some numerical illustrations and related comparisons.<\/jats:p>","DOI":"10.1155\/2020\/6079507","type":"journal-article","created":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T23:31:20Z","timestamp":1584401480000},"page":"1-14","source":"Crossref","is-referenced-by-count":6,"title":["Optimal Decay Rate Estimates of a Nonlinear Viscoelastic Kirchhoff Plate"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4507-8170","authenticated-orcid":true,"given":"Baowei","family":"Feng","sequence":"first","affiliation":[{"name":"Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4280-9321","authenticated-orcid":true,"given":"Mostafa","family":"Zahri","sequence":"additional","affiliation":[{"name":"College of Sciences, Department of Mathematics, Research Group MASEP, University of 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