{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:16:11Z","timestamp":1764173771128,"version":"3.41.2"},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,9,19]],"date-time":"2011-09-19T00:00:00Z","timestamp":1316390400000},"content-version":"vor","delay-in-days":261,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11071266"],"award-info":[{"award-number":["11071266"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>We deal with the extinction of the solutions of the initial\u2010boundary value problem of the discrete <jats:italic>p<\/jats:italic>\u2010Laplacian equation with absorption <jats:italic>u<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub> = \u0394<jats:sub><jats:italic>p<\/jats:italic>,<jats:italic>\u03c9<\/jats:italic><\/jats:sub><jats:italic>u<\/jats:italic> \u2212 <jats:italic>u<\/jats:italic><jats:sup><jats:italic>q<\/jats:italic><\/jats:sup> with <jats:italic>p<\/jats:italic> &gt; 1, <jats:italic>q<\/jats:italic> &gt; 0, which is said to be the discrete <jats:italic>p<\/jats:italic>\u2010Laplacian equation on weighted graphs. For 0 &lt; <jats:italic>q<\/jats:italic> &lt; 1, we show that the nontrivial solution becomes extinction in finite time while it remains strictly positive for <jats:italic>p<\/jats:italic> \u2265 2, <jats:italic>q<\/jats:italic> \u2265 1 and <jats:italic>q<\/jats:italic> \u2265 <jats:italic>p<\/jats:italic> \u2212 1. Finally, a numerical experiment on a simple graph with standard weight is given.<\/jats:p>","DOI":"10.1155\/2011\/937079","type":"journal-article","created":{"date-parts":[[2011,9,19]],"date-time":"2011-09-19T20:24:31Z","timestamp":1316463871000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Extinction and Positivity of the Solutions for a <i>p<\/i>\u2010Laplacian Equation with Absorption on Graphs"],"prefix":"10.1155","volume":"2011","author":[{"given":"Qiao","family":"Xin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunlai","family":"Mu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dengming","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,9,19]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139903432743"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/0150055"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/0151051"},{"key":"e_1_2_7_4_2","first-page":"31","article-title":"Discrete potentials on an infinite network","volume":"13","author":"Yamasaki M.","year":"1979","journal-title":"Memoirs of the Faculty of Literature and Science. 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