Fractional-order operators: Boundary problems, heat equationsThe first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential ...
In this paper we study a fractional stochastic heat equation on Rd (d 〉 1) with additive noise /t u(t, x) = Dα/δ u(t, x)+ b(u(t, x) ) + WH (t, x) where D α/δ is a nonlocal fractional differential operator and W H is a Gaussian-colored noise. We show the ...
This paper is devoted to the rigorous derivation of the macroscopic limit of a Vlasov- Fokker-Planck equation in which the Laplacian is replaced by a fractional Laplacian. The evolution of the density is governed by a fractional heat equation with the addition of a convective term coming from ...
Weak solutions for a fractionalp-Laplacian equation with sign-changing potential In this paper, we use some critical point theorems to discuss the existence of weak solutions for the fractional p-Laplacian equation in where , , is a pa... Jiafa,Xu,Zhongli,... - 《Complex Variables Theory &...
设α 0 ,分数阶Laplacian 微分算子 −∆ 通过Fourier 变换定义为: ( ) α 2α −∆ ξ ξ ξ u ,t u ,t . (( ) ( )) ( ) 不可压缩Navier-Stokes 方程在气象学、海洋学和地球物理学等众多领域中有着广泛的应用。由于地 球自转对空气流及海洋流产生着旋转效应与周期效应,因此...
Actually, Theorem 2.5, Theorem 2.8 tell us that, not only the parameter q but also α (the order of the fractional Laplacian operator) and p (the a-priori assumption) all affect the convergence results. Moreover, the demarcation of the parameter q here is pα+1 for the a-posteriori ...
Radial symmetry of standing waves for nonlinear fractional Laplacian Hardy-Schrdinger systems In this paper, by applying the method of moving planes, we conclude the conclusions for the radial symmetry of standing waves for a nonlinear Schrdinger eq... G Wang,X Ren,Z Bai,... - 《Applied Mat...
Multiple solutions of a p-Laplacian model involving a fractional derivative In this paper, we study the -Laplacian model involving the Caputo fractional derivative with Dirichlet-Neumann boundary conditions. Using a fixed point the... X Liu,J Mei,W Ge - 《Advances in Difference Equations》 被引...
The said operator combines an inverse fractional Laplacian with a Helmholtz-like decomposition and weighted recombination. Classical fBm's can be obtained by ... PD Tafti,M Unser - 《Multiscale Modeling & Simulation》 被引量: 32发表: 2010年 An inverse problem for a generalized fractional diffusio...
( x , t ) , the evolution equation reads t h + ( Δ ) s Φ ( h ) = 0 , while the temperature is defined as u : = Φ ( h ) : = max { h L , 0 } for some constant L > 0 called the latent heat, and ( Δ ) s stands for the fractional Laplacian with exponent s ...