NONLINEAR FOKKER-PLANCK EQUATIONS WITH TIME-DEPENDENT COEFFICIENTS

被引：5

作者：

Barbu, Viorelc ^{[1
]}

Rockner, Michael ^{[2
]}

机构：

[1] Romanian Acad, Octav Mayer Inst Math, Iasi, Romania

[2] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2023年 / 55卷 / 01期

关键词：

Fokker-Planck equation; Cauchy problem; stochastic differential equation; Sobolev space;

D O I：

10.1137/21M145481X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An operator-based approach is used here to prove the existence and uniqueness of u(t, x)) + div(b(t, x, u(t, x))u(t, x)) = 0 in (0, oo) \times Rd, u(0, x) = u0(x), x \in Rd in the Sobolev space proved also that if u0 is a density of a probability measure, so is u(t, & BULL;) for all t \geq 0. Moreover, we construct a weak solution to the McKean-Vlasov SDE associated with the Fokker-Planck equation such that u(t) is the density of its time marginal law.

引用

页码：1 / 18

页数：18

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