论文标题
带有Caputo衍生物的细胞扩散方程的逆问题
Inverse problem for a subdiffusion equation with the Caputo derivative
论文作者
论文摘要
该文章研究了用Caputo分数衍生物确定细胞扩散方程的右侧的反问题，其椭圆形部分具有最一般的形式，并在n维圆环T中定义 n。傅立叶方法用于证明定理关于初始界价值问题的经典解决方案的存在和唯一性，以及方程未知右侧的唯一重建。根据最初功能和其他条件的要求，可以将经典傅立叶方法应用于所考虑的逆问题。
The article investigates an inverse problem of determining the right-hand side of a subdiffusion equation with Caputo fractional derivative whose elliptic part has the most general form and is defined on an N-dimensional torus T N . The Fourier method is used to prove theorems on the existence and uniqueness of the classical solution of the initial-boundary value problem and on the unique reconstruction of the unknown right-hand side of the equation. Requirements for the initial function and for the additional condition are established under which the classical Fourier method can be applied to the inverse problem under consideration.
