{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T13:22:40Z","timestamp":1762262560672,"version":"build-2065373602"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"published-print":{"date-parts":[[2015,7,23]]},"abstract":"<jats:p>\n                    We consider variational inequality solutions with prescribed gradient constraints for first order linear boundary value problems. For operators with coefficients only in\n                    <jats:inline-formula>\n                      <jats:tex-math>L^2<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , we show the existence and uniqueness of the solution by using a combination of parabolic regularization with a penalization in the nonlinear diffusion coefficient. We also prove the continuous dependence of the solution with respect to the data, as well as, in a coercive case, the asymptotic stabilization as time\n                    <jats:inline-formula>\n                      <jats:tex-math>t \\rightarrow + \\infty<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    towards the stationary solution. In a particular situation, motivated by the transported sandpile problem, we give sufficient conditions for the equivalence of the first order problem with gradient constraint with a two obstacles problem, the obstacles being the signed distances to the boundary. This equivalence, in special conditions, illustrates also the possible stabilization of the solution in finite time.\n                  <\/jats:p>","DOI":"10.4171\/pm\/1963","type":"journal-article","created":{"date-parts":[[2015,7,23]],"date-time":"2015-07-23T17:45:03Z","timestamp":1437673503000},"page":"161-192","source":"Crossref","is-referenced-by-count":0,"title":["Solutions for linear conservation laws with gradient constraint"],"prefix":"10.4171","volume":"72","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8438-0749","authenticated-orcid":false,"given":"Jos\u00e9 Francisco","family":"Rodrigues","sequence":"first","affiliation":[{"name":"FC Universidade de Lisboa, Portugal"}]},{"given":"Lisa","family":"Santos","sequence":"additional","affiliation":[{"name":"Universidade do Minho, Braga, Portugal"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/PM\/1963","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T13:12:36Z","timestamp":1762261956000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/1963"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,23]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.4171\/pm\/1963","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"type":"print","value":"0032-5155"},{"type":"electronic","value":"1662-2758"}],"subject":[],"published":{"date-parts":[[2015,7,23]]}}}