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In the case where the inhibitor\u2019s response to the activator\u2019s growth is rather weak, then the shadow system of the Gierer\u2013Meinhardt model is reduced to a single though non-local equation whose dynamics is thoroughly investigated throughout the manuscript. The main focus is on the derivation of blow-up results for this non-local equation, which can be interpreted as instability patterns of the shadow system. In particular, a diffusion-driven instability (DDI), or Turing instability, in the neighbourhood of a constant stationary solution, which then is destabilised via diffusion-driven blow-up, is observed. The latter indicates the formation of some unstable patterns, whilst some stability results of global-in-time solutions towards non-constant steady states guarantee the occurrence of some stable patterns. Most of the theoretical results are verified numerically, whilst the numerical approach is also used to exhibit the dynamics of the shadow system when analytical methods fail.<\/jats:p>","DOI":"10.1007\/s00332-020-09664-3","type":"journal-article","created":{"date-parts":[[2020,12,18]],"date-time":"2020-12-18T12:03:37Z","timestamp":1608293017000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Dynamics of Shadow System of a Singular Gierer\u2013Meinhardt System on an Evolving Domain"],"prefix":"10.1007","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9743-8636","authenticated-orcid":false,"given":"Nikos I.","family":"Kavallaris","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raquel","family":"Barreira","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9511-8903","authenticated-orcid":false,"given":"Anotida","family":"Madzvamuse","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,12,18]]},"reference":[{"key":"9664_CR1","doi-asserted-by":"publisher","first-page":"1401","DOI":"10.1016\/j.jmaa.2018.11.082","volume":"472","author":"A Bobrowski","year":"2019","unstructured":"Bobrowski, A., Kunze, M.: Irregular convergence of mild solutions of semilinear equations. 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