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Math."],"published-print":{"date-parts":[[2026,4]]},"abstract":"Abstract<\/jats:title>\n \n We study the spatially homogeneous granular medium equation\n \n \n $$\\begin{aligned} \\partial _t\\mu =\\textrm{div}(\\mu \\nabla V)+\\textrm{div}(\\mu (\\nabla W *\\mu ))+\\Delta \\mu \\,, \\end{aligned}$$<\/jats:tex-math>\n \n \n \n \n \n \n \n \u2202<\/mml:mi>\n t<\/mml:mi>\n <\/mml:msub>\n \u03bc<\/mml:mi>\n =<\/mml:mo>\n div<\/mml:mtext>\n \n (<\/mml:mo>\n \u03bc<\/mml:mi>\n \u2207<\/mml:mi>\n V<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n +<\/mml:mo>\n div<\/mml:mtext>\n \n (<\/mml:mo>\n \u03bc<\/mml:mi>\n \n (<\/mml:mo>\n \u2207<\/mml:mi>\n W<\/mml:mi>\n \n \u2217<\/mml:mo>\n \u03bc<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n +<\/mml:mo>\n \u0394<\/mml:mi>\n \u03bc<\/mml:mi>\n \n ,<\/mml:mo>\n <\/mml:mrow>\n <\/mml:mtd>\n <\/mml:mtr>\n <\/mml:mtable>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:disp-formula>\n within a large and natural class of the confinement potentials\n V<\/jats:italic>\n and interaction potentials\n W<\/jats:italic>\n . The considered problem do not need to assume that\n \n \n $$\\nabla V$$<\/jats:tex-math>\n \n \n \u2207<\/mml:mi>\n V<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n or\n \n \n $$\\nabla W$$<\/jats:tex-math>\n \n \n \u2207<\/mml:mi>\n W<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n are globally Lipschitz. With the aim of providing particle approximation of solutions, we design efficient forward-backward splitting algorithms. Sharp convergence rates in terms of the Wasserstein distance are provided.\n <\/jats:p>","DOI":"10.1007\/s00211-025-01516-0","type":"journal-article","created":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T10:36:24Z","timestamp":1770633384000},"page":"411-454","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations"],"prefix":"10.1007","volume":"158","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-8311-6301","authenticated-orcid":false,"given":"Matej","family":"Benko","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2053-5988","authenticated-orcid":false,"given":"Iwona","family":"Chlebicka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9931-7945","authenticated-orcid":false,"given":"J\u00f8rgen","family":"Endal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3691-9372","authenticated-orcid":false,"given":"B\u0142a\u017cej","family":"Miasojedow","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,2,9]]},"reference":[{"issue":"1","key":"1516_CR1","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1007\/s00211-023-01388-2","volume":"156","author":"A Aggarwal","year":"2024","unstructured":"Aggarwal, A., Holden, H., Vaidya, G.: On the accuracy of the finite volume approximations to nonlocal conservation laws. 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