排序方式: 共有12条查询结果,搜索用时 15 毫秒
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A. I. Noarov 《Siberian Mathematical Journal》2014,55(3):465-470
The stationary Fokker-Planck-Kolmogorov equation with complex diffusion coefficients and a complex vector-field is examined on a torus. Under suitable conditions for the diffusion coefficients, it is proven that a nontrivial solution exists and the solution space is multidimensional in some cases. 相似文献
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A. I. Noarov 《Differential Equations》2009,45(2):197-208
We study the stationary Focker-Planck equation Δu ? div(u f) = 0 with a given vector field f of the class C 0 ∞ (R n ) on the basis of a fixed point principle that generalizes the contraction mapping method. Next, we introduce a parameter in the equation and prove the unique solvability of the equation Δu ? div(uγ f) = 0 with the parameter in the class of positive slowly increasing functions. We reveal the analytic dependence of the positive solution u on the parameter γ. Pointwise estimates for positive solutions are proved. 相似文献
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A. I. Noarov 《Siberian Mathematical Journal》2012,53(6):1115-1118
We examine the functional-differential equation Δu(x) — div(u(H(x))f (x)) = 0 on a torus which is a generalization of the stationary Fokker-Planck equation. Under sufficiently general assumptions on the vector field f and the map H, we prove the existence of a nontrivial solution. In some cases the subspace of solutions is established to be multidimensional. 相似文献
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A. I. Noarov 《Computational Mathematics and Mathematical Physics》2011,51(4):602-608
A projection-type condition is discussed that is sufficient for the stationary Fokker-Planck equation Δu - div(u
f) = 0 to be solvable within a class of probability density functions. Based on existence theorems and estimates of positive
solutions obtained by the author, a fairly large class of vector fields f satisfying this condition is proposed. 相似文献
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A. I. Noarov 《Theoretical and Mathematical Physics》2016,189(3):1796-1805
We investigate the Fokker–Planck equation on an infinite cylindrical surface and in an infinite strip with reflecting boundary conditions, prove the existence of a positive (not necessarily integrable) solution, and derive various conditions on the vector field f that are sufficient for the existence of a solution that is the probability density. In particular, these conditions are satisfied for some vector fields f with integral trajectories going to infinity. 相似文献
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Ukrainian Mathematical Journal - We prove inequalities connecting a flow through the (n?1)-dimensional surface S of a smooth solenoidal vector field with its Lp(U)-norm (U is an n-dimensional... 相似文献
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A. I. Noarov 《Computational Mathematics and Mathematical Physics》2006,46(8):1341-1348
The Lorenz system perturbed by noise and its invariant measure whose density obeys the stationary Fokker-Planck equation are analyzed numerically. A linear functional of the invariant measure is considered, and its variation caused by a variation in the right-hand side of the Lorenz system is calculated. A small (in modulus) external perturbation is calculated under which the strange attractor of the Lorenz system degenerates into a stable fixed point. 相似文献