论文标题
半线性次要方程的Galerkin方案的误差，具有时间相关系数和非平滑数据
Error of the Galerkin scheme for a semilinear subdiffusion equation with time-dependent coefficients and nonsmooth data
论文作者
论文摘要
我们研究了在没有非平滑初始数据的情况下，研究了（半分化）Galerkin方法的误差。扩散系数允许依赖时间。众所周知，在这种抛物线问题下，时间降低时空间误差会增加。该时间依赖性的速率是分数参数和初始条件的规律性的函数。我们使用能量方法在弱和自然假设下在扩散率上找到最佳界限。首先，我们证明了线性问题的结果，然后使用“冷冻的非线性”技术，再加上格朗沃尔不平等的各种概括，将结果带入半线性案例。本文以支持理论结果的数值插图结尾。
We investigate the error of the (semidiscrete) Galerkin method applied to a semilinear subdiffusion equation in the presence of a nonsmooth initial data. The diffusion coefficient is allowed to depend on time. It is well-known that in such parabolic problems the spatial error increases when time decreases. The rate of this time-dependency is a function of the fractional parameter and the regularity of the initial condition. We use the energy method to find optimal bounds on the error under weak and natural assumptions on the diffusivity. First, we prove the result for the linear problem and then use the "frozen nonlinearity" technique coupled with various generalizations of Gronwall inequality to carry the result to the semilinear case. The paper ends with numerical illustrations supporting the theoretical results.
