Nonlinear Fokker–Planck Equations with Time-Dependent Coefficients
Barbu, Viorelc
Barbu
Viorelc
Röckner, Michael
Röckner
Michael
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.
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1-18
1-18
Society for Industrial and Applied Mathematics
2023