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Appl. 473(2) ( 2019 ) 1122\u20131154). In the present work, we show how all the anisotropic exponents of nonlinearity and all anisotropic coefficients should interact with the problem data for the solutions of this problem display exponential and polynomial time-decays. We also establish the conditions for the solutions of this problem to blow-up in a finite time in three different cases: problem without convection, full anisotropic problem, and the problem with isotropic relaxation.<\/jats:p>","DOI":"10.3233\/asy-201597","type":"journal-article","created":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:15:38Z","timestamp":1579259738000},"page":"125-157","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Kelvin\u2013Voigt equations with anisotropic diffusion, relaxation and damping: Blow-up\u00a0and large time behavior"],"prefix":"10.1177","volume":"121","author":[{"given":"S.","family":"Antontsev","sequence":"first","affiliation":[{"name":"CMAFCIO, Universidade de Lisboa, Portugal"},{"name":"Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russia. 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