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Theor."],"published-print":{"date-parts":[[2020,4,17]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The present paper studies, strictly within the theory of distributions, the propagation of travelling waves with a distributional profile in one-dimensional models ruled by convection\u2013diffusion\u2013reaction equations. By applying a product of distributions (not defined by approximation processes), a rigorous concept of a solution which extends the classical solution concept is defined. As a consequence we establish necessary and sufficient conditions for the propagation of a distributional profile. The use of these conditions enable us to see the appearance of shock waves, delta waves and also delta shock travelling waves. The main ideas and formulas needed for multiplying distributions are included for the reader\u2019s convenience.<\/jats:p>","DOI":"10.1088\/1751-8121\/ab7c1d","type":"journal-article","created":{"date-parts":[[2020,3,3]],"date-time":"2020-03-03T17:30:24Z","timestamp":1583256624000},"page":"155202","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["New singular travelling waves for convection\u2013diffusion\u2013reaction equations"],"prefix":"10.1088","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5662-4419","authenticated-orcid":false,"given":"C O R","family":"Sarrico","sequence":"first","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2020,3,26]]},"reference":[{"key":"aab7c1dbib1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-0307-0_2","type":"book","article-title":"The influence of the advection on the propagation of fronts in reaction-diffusion equations","author":"Berestychi","year":"2002"},{"key":"aab7c1dbib2","doi-asserted-by":"publisher","author":"Gilding","year":"2004","DOI":"10.1007\/978-3-0348-7964-4","type":"book"},{"key":"aab7c1dbib3","doi-asserted-by":"publisher","first-page":"3367","DOI":"10.1088\/0305-4470\/38\/15\/009","type":"journal-article","article-title":"A Fisher\/KPP-type equation with density dependent diffusion and convection: travelling wave solutions","volume":"38","author":"Gilding","year":"2005","journal-title":"J. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2019-10-23","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2020-03-03","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2020-03-26","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}