{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T04:07:07Z","timestamp":1762056427603,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T00:00:00Z","timestamp":1656547200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The goal of this study is to provide an analysis of a Fisher-KPP non-linear reaction problem with a higher-order diffusion and a non-linear advection. We study the existence and uniqueness of solutions together with asymptotic solutions and positivity conditions. We show the existence of instabilities based on a shooting method approach. Afterwards, we study the existence and uniqueness of solutions as an abstract evolution of a bounded continuous single parametric (t) semigroup. Asymptotic solutions based on a Hamilton\u2013Jacobi equation are then analyzed. Finally, the conditions required to ensure a comparison principle are explored supported by the existence of a positive maximal kernel.<\/jats:p>","DOI":"10.3390\/e24070915","type":"journal-article","created":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T20:53:02Z","timestamp":1656622382000},"page":"915","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Heterogeneous Diffusion and Nonlinear Advection in a One-Dimensional Fisher-KPP Problem"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4677-0970","authenticated-orcid":false,"given":"Jos\u00e9 Luis D\u00edaz","family":"Palencia","sequence":"first","affiliation":[{"name":"Department of Mathematics and Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain"},{"name":"Technology Programs, Schiller International University, Calle Serrano 156, 28002 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saeed ur","family":"Rahman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Abbottabad 22060, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio Naranjo","family":"Redondo","sequence":"additional","affiliation":[{"name":"Technology Programs, Schiller International University, Calle Serrano 156, 28002 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Okubo, A., and Levin, S.A. 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