论文标题
在偏斜的分数扩散反应反应方程上
On the Skewed Fractional Diffusion Advection Reaction Equation on the Interval
论文作者
论文摘要
本文提供了提高分数方程的规律性的技术，并解决了关于偏斜（双面）分数扩散反应方程（FDARE）的一维同质边界问题问题的基本问题，并在界间间隔可变系数。建立了真实（经典）解决方案以及规范估计的存在，并找到了确切的规律性结合；同样，溶液的结构是拆开的，捕获了规律性，奇异性和溶液的其他特征的本质。关键分析在于探索高斯高几何函数的属性，求解耦合的ABEL积分方程和主导的单数积分方程，并将从分数Sobolev空间与H $ \ ddot {\ text {O}} $ LDERAIN空间相连的功能，从而将其连接起来。
This article provides techniques of raising the regularity of fractional order equations and resolves fundamental questions on the one-dimensional homogeneous boundary-value problem of skewed (double-sided) fractional diffusion advection reaction equation (FDARE) with variable coefficients on the bounded interval. The existence of the true (classical) solution together with norm estimation is established and the precise regularity bound is found; also, the structure of the solution is unraveled, capturing the essence of regularity, singularity, and other features of the solution. The key analysis lies in exploring the properties of Gauss hypergeometric functions, solving coupled Abel integral equations and dominant singular integral equations, and connecting the functions from fractional Sobolev spaces to the ones from H$\ddot{\text{o}}$lderian spaces that admit integrable singularities at the endpoints.
