{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:51:32Z","timestamp":1777449092881,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2013,12,1]],"date-time":"2013-12-01T00:00:00Z","timestamp":1385856000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p>We give an approach to exponential stability within the framework of evolutionary equations due to Picard [Math. Methods Appl. Sci. 32(14) (2009), 1768\u20131803]. We derive sufficient conditions for exponential stability in terms of the material law operator which is defined via an analytic and bounded operator-valued function and give an estimate for the expected decay rate. The results are illustrated by three examples: differential-algebraic equations, partial differential equations with finite delay and parabolic integro-differential equations.<\/jats:p>","DOI":"10.3233\/asy-131181","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:30:33Z","timestamp":1575055833000},"page":"179-197","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":9,"title":["Exponential stability for linear evolutionary equations"],"prefix":"10.1177","volume":"85","author":[{"given":"Sascha","family":"Trostorff","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Analysis, Fachrichtung Mathematik, Technische Universit\u00e4t Dresden, Dresden, Germany. E-mail: sascha.trostorff@tu-dresden.de"}]}],"member":"179","published-online":{"date-parts":[[2013,12,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131181","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131181","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:01Z","timestamp":1777380001000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-131181"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2013,12]]}},"alternative-id":["10.3233\/ASY-131181"],"URL":"https:\/\/doi.org\/10.3233\/asy-131181","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12]]}}}