{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:53:26Z","timestamp":1777449206580,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2015,2,1]],"date-time":"2015-02-01T00:00:00Z","timestamp":1422748800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2015,2]]},"abstract":"<jats:p>We deal with the existence of nonnegative solutions to parabolic problems which are singular in the u variable whose model is<\/jats:p>\n                  <jats:p>\n                    u\n                    <jats:sub>t<\/jats:sub>\n                    \u2212\u0394\n                    <jats:sub>p<\/jats:sub>\n                    u=f(x,t)(1\/u\n                    <jats:sup>\u03b8<\/jats:sup>\n                    +1)\u2003in \u03a9\u00d7(0,T),\n                  <\/jats:p>\n                  <jats:p>u(x,t)=0\u2003on \u2202\u03a9\u00d7(0,T),<\/jats:p>\n                  <jats:p>\n                    u(x,0)=u\n                    <jats:sub>0<\/jats:sub>\n                    (x)\u2003in \u03a9.\n                  <\/jats:p>\n                  <jats:p>\n                    Here \u03a9 is a bounded open subset of R\n                    <jats:sup>N<\/jats:sup>\n                    , N\u22652, 0&lt;T&lt;+\u221e, \u03b8&gt;0, \u0394\n                    <jats:sub>p<\/jats:sub>\n                    u=div\u2009(|\u2207u|\n                    <jats:sup>p\u22122<\/jats:sup>\n                    \u2207u) with p&gt;1.\n                  <\/jats:p>\n                  <jats:p>\n                    As far as the data are concerned, we assume f(x,t)\u2208L\n                    <jats:sup>r<\/jats:sup>\n                    (0,T;L\n                    <jats:sup>m<\/jats:sup>\n                    (\u03a9)), with 1\/r+N\/pm&lt;1, f(x,t)\u22650 a.e. in \u03a9\u00d7(0,T) and u\n                    <jats:sub>0<\/jats:sub>\n                    (x)\u22650 a.e. in \u03a9.\n                  <\/jats:p>\n                  <jats:p>\n                    We consider also the case where the right-hand side depends on the gradient of the solution. In this last case the model of the right-hand side is F(x,t,u,\u2207u)=(f(x,t)+D|\u2207u|\n                    <jats:sup>q<\/jats:sup>\n                    )\/u\n                    <jats:sup>\u03b8<\/jats:sup>\n                    , with \u03b8&gt;0, D&gt;0, 1&lt;q&lt;p and f(x,t) as before.\n                  <\/jats:p>","DOI":"10.3233\/asy-141257","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:37:40Z","timestamp":1575056260000},"page":"147-183","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":10,"title":["Nonnegative solutions for a class of singular parabolic problems involving p-Laplacian"],"prefix":"10.1177","volume":"91","author":[{"given":"Ida","family":"de Bonis","sequence":"first","affiliation":[{"name":"Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Universit\u00e0 di Roma, Via A. Scarpa 16, 00161 Roma, Italy. E-mails: ida.debonis@sbai.uniroma1.it, daniela.giachetti@sbai.uniroma1.it"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniela","family":"Giachetti","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Universit\u00e0 di Roma, Via A. Scarpa 16, 00161 Roma, Italy. E-mails: ida.debonis@sbai.uniroma1.it, daniela.giachetti@sbai.uniroma1.it"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,2,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141257","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-141257","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:21Z","timestamp":1777380021000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-141257"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,2]]}},"alternative-id":["10.3233\/ASY-141257"],"URL":"https:\/\/doi.org\/10.3233\/asy-141257","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2]]}}}