{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T13:22:21Z","timestamp":1762262541997,"version":"build-2065373602"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"published-print":{"date-parts":[[2023,5,17]]},"abstract":"<jats:p>\n                    The Oort\u2013Hulst\u2013Safronov equation is a relevant population balance model. Its discrete form, developed by Pavel Dubovski, is the main focus of our analysis. The existence and density conservation are established for non-negative symmetric coagulation rates satisfying\n                    <jats:inline-formula>\n                      <jats:tex-math>V_{i,j} \\leqslant i+j<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ,\n                    <jats:inline-formula>\n                      <jats:tex-math>\\forall i,j \\in \\mathbb{N}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    . Differentiability of the solutions is investigated for kernels with\n                    <jats:inline-formula>\n                      <jats:tex-math>V_{i,j} \\leqslant i^{\\alpha}+j^{\\alpha}<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    where\n                    <jats:inline-formula>\n                      <jats:tex-math>0 \\leqslant \\alpha \\leqslant 1<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    with initial conditions with bounded\n                    <jats:inline-formula>\n                      <jats:tex-math>(1+\\alpha)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -th moments. The article ends with a uniqueness result under an additional assumption on the coagulation kernel and the boundedness of the second moment.\n                  <\/jats:p>","DOI":"10.4171\/pm\/2103","type":"journal-article","created":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T17:45:35Z","timestamp":1684345535000},"page":"343-367","source":"Crossref","is-referenced-by-count":0,"title":["Theoretical analysis of a discrete population balance model with sum kernel"],"prefix":"10.4171","volume":"80","author":[{"given":"Sonali","family":"Kaushik","sequence":"first","affiliation":[{"name":"Birla Institute of Technology and Science, Pilani, Rajasthan, India"}]},{"given":"Rajesh","family":"Kumar","sequence":"additional","affiliation":[{"name":"Birla Institute of Technology and Science, Pilani, Rajasthan, India"}]},{"given":"Fernando P.","family":"da Costa","sequence":"additional","affiliation":[{"name":"Universidade Aberta, Lisboa"},{"name":"Universidade de Lisboa, Portugal"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T13:13:03Z","timestamp":1762261983000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/2103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,17]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.4171\/pm\/2103","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"type":"print","value":"0032-5155"},{"type":"electronic","value":"1662-2758"}],"subject":[],"published":{"date-parts":[[2023,5,17]]}}}