{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:47:21Z","timestamp":1747198041984,"version":"3.40.5"},"reference-count":55,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,1,1]]},"abstract":"Abstract<\/jats:title>The initial value problem for an evolution equation of typev<\/m:mi>\u2032<\/m:mo><\/m:msup>+<\/m:mo>A<\/m:mi>\u2062<\/m:mo>v<\/m:mi><\/m:mrow>+<\/m:mo>B<\/m:mi>\u2062<\/m:mo>K<\/m:mi>\u2062<\/m:mo>v<\/m:mi><\/m:mrow><\/m:mrow>=<\/m:mo>f<\/m:mi><\/m:mrow><\/m:math>{v^{\\prime}+Av+BKv=f}<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>is studied, whereA<\/m:mi>:<\/m:mo>V<\/m:mi>A<\/m:mi><\/m:msub>\u2192<\/m:mo>V<\/m:mi>A<\/m:mi>\u2032<\/m:mo><\/m:msubsup><\/m:mrow><\/m:mrow><\/m:math>{A:V_{A}\\to V_{A}^{\\prime}}<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>is a monotone, coercive operator and whereB<\/m:mi>:<\/m:mo>V<\/m:mi>B<\/m:mi><\/m:msub>\u2192<\/m:mo>V<\/m:mi>B<\/m:mi>\u2032<\/m:mo><\/m:msubsup><\/m:mrow><\/m:mrow><\/m:math>{B:V_{B}\\to V_{B}^{\\prime}}<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>induces an inner product. The Banach spaceV<\/m:mi>A<\/m:mi><\/m:msub><\/m:math>{V_{A}}<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>is not required to be embedded inV<\/m:mi>B<\/m:mi><\/m:msub><\/m:math>{V_{B}}<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>or vice versa. The operatorK<\/jats:italic>incorporates a Volterra integral operator in time of convolution type with an exponentially decaying kernel. Existence of a global-in-time solution is shown by proving convergence of a suitable time discretisation. Moreover, uniqueness as well as stability results are proved. Appropriate integration-by-parts formulae are a key ingredient for the analysis.<\/jats:p>","DOI":"10.1515\/cmam-2018-0268","type":"journal-article","created":{"date-parts":[[2018,11,21]],"date-time":"2018-11-21T09:05:22Z","timestamp":1542791122000},"page":"89-108","source":"Crossref","is-referenced-by-count":1,"title":["Nonlinear Evolution Equations with Exponentially Decaying Memory: Existence via Time Discretisation, Uniqueness, and Stability"],"prefix":"10.1515","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0270-6491","authenticated-orcid":false,"given":"Andr\u00e9","family":"Eikmeier","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Mathematik , Technische Universit\u00e4t Berlin , Stra\u00dfe des 17. 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