Operator-splitting schemes for degenerate, non-local, conservative-dissipative systems
نویسندگان
چکیده
<p style='text-indent:20px;'>In this paper, we develop a natural operator-splitting variational scheme for general class of non-local, degenerate conservative-dissipative evolutionary equations. The splitting-scheme consists two phases: conservative (transport) phase and dissipative (diffusion) phase. first is solved exactly using the method characteristic DiPerna-Lions theory while second approximately JKO-type that minimizes an energy functional with respect to certain Kantorovich optimal transport cost functional. In addition, also introduce entropic-regularisation scheme. We prove convergence both schemes weak solution equation. illustrate generality our work by providing number examples, including kinetic Fokker-Planck equation (regularized) Vlasov-Poisson-Fokker-Planck equation.</p>
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2022
ISSN: ['1553-5231', '1078-0947']
DOI: https://doi.org/10.3934/dcds.2022109