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The first phase is solved exactly using the method of characteristic and DiPerna-Lions theory while the second phase is solved approximately using a JKO-type variational scheme that minimizes an energy functional with respect to a certain Kantorovich optimal transport cost functional. In addition, we also introduce an entropic-regularisation of the scheme. We prove the convergence of both schemes to a weak solution of the evolutionary equation. We illustrate the generality of our work by providing a number of examples, including the kinetic Fokker-Planck equation and the (regularized) Vlasov-Poisson-Fokker-Planck equation.<\/p><\/jats:p>","DOI":"10.3934\/dcds.2022109","type":"journal-article","created":{"date-parts":[[2022,8,5]],"date-time":"2022-08-05T10:11:59Z","timestamp":1659694319000},"page":"5453","source":"Crossref","is-referenced-by-count":2,"title":["Operator-splitting schemes for degenerate, non-local, conservative-dissipative systems"],"prefix":"10.3934","volume":"42","author":[{"given":"Daniel","family":"Adams","sequence":"first","affiliation":[{"name":"Maxwell Institute for Mathematical Sciences and School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, Scotland"}]},{"given":"Manh Hong","family":"Duong","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Birmingham, Birmingham B15 2TT, England"}]},{"given":"Gon\u00e7alo dos","family":"Reis","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Edinburgh, Mayfield Rd, Edinburgh, EH9 3FD, Scotland"}]}],"member":"2321","reference":[{"key":"key-10.3934\/dcds.2022109-1","doi-asserted-by":"publisher","unstructured":"S. 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