论文标题
带有任意椭圆差算子的时间分数次扩散方程的初始符号值问题
Initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary elliptic differential operator
论文作者
论文摘要
考虑使用任意阶差异差异操作员的时间分解子扩散方程的初始有限值问题。经典傅立叶方法证明了构成问题的经典解决方案的独特性和存在。指示了方程的初始功能和方程右侧的足够条件，在此条件下，相应的傅立叶级数绝对均匀地收敛。如果在n维圆环上存在初始有限的价值问题，则可以很容易地看到这些条件不仅足够，而且是必要的。
An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the classical Fourier method. Sufficient conditions for the initial function and for the right-hand side of the equation are indicated, under which the corresponding Fourier series converge absolutely and uniformly. In the case of an initial-boundary value problem on N-dimensional torus, one can easily see that these conditions are not only sufficient, but also necessary.
