Existence of solution for a fractional advection dispersion equation in R-N
Existence of solution for a fractional advection dispersion equation in R-N
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DOI：
10.1016/j.apm.2014.02.002
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发表时间：
2014-08
影响因子：
5
通讯作者：
Quanguo Zhang;Hong‐Rui Sun;Yaning Li
中科院分区：
文献类型：
--
作者：
Quanguo Zhang;Hong‐Rui Sun;Yaning Li
本文讨论了一类分数阶对流扩散方程-解的存在性| θ| = 1 D θ D θ β uM（d θ）+ B（x）u= f（x，u），x∈ RN，u∈ H α（RN），其中N> 1，inf RN B（x）> 0，f：RN × R→ R是连续的，常数β∈（0，1），α= β+12，M（d θ）是RN中单位球面上的Borel概率测度，D θ β表示在单位向量θ方向上的β阶方向分数导数。利用山路引理和迭代技巧研究了当M是对称和非对称时问题解的存在性。本文的主要结果强调了一般Borel概率测度所起的中心作用。
This paper is concerned with the existence of solution to the following fractional advection dispersion equation-∫| θ|= 1 D θ D θ β uM (d θ)+ b (x) u= f (x, u), x∈ R N, u∈ H α (R N), where N> 1, inf R N b (x)> 0, f: R N× R→ R is continuous, the constant β∈(0, 1), α= β+ 1 2, M (d θ) is a Borel probability measure on the unit sphere in R N, D θ β denotes directional fractional derivative of order β in the direction of the unit vector θ. We focus our investigation on the existence of solution to the problem when M is symmetric and nonsymmetric by the Mountain Pass theorem and iterative technique. The main results of this paper emphasize the central role played by the general Borel probability measure.