由Dunkl算子生成的一个反源问题
One inverse source problem generated by the Dunkl operator
AI总结：
本文研究了由Dunkl算子生成的时间分数阶伪抛物型方程，建立了正问题的适定性并推导了解的显式公式，进而证明了反源问题解的存在唯一性及对数据的连续依赖性，并通过数值测试进行验证。
摘要：
本文旨在研究由Dunkl算子生成的时间分数阶伪抛物型方程。考虑了正问题并建立了其适定性。特别地，在Sobolev型空间中获得了先验估计，并推导了问题解的显式公式。此处我们还处理了左侧Caputo分数阶时间导数。作为应用，我们研究了一个反源问题。证明了解的存在性与唯一性。此外，我们证明了解对连续依赖于初始和附加数据，并以数值测试作结。
英文摘要：
The aim of this paper is to study time-fractional pseudo-parabolic type equations generated by the Dunkl operator. The forward problem is considered and its well-posedness is established. In particular, a prior estimates are obtained in the Sobolev type spaces and, explicit formulas for solutions of the problems are derived. Here we also deal with the left-sided Caputo fractional time derivative. As an application, we investigate an inverse source problem. Existence and uniqueness of the solution is proved. Moreover, we show that a solution pair is continuously depending on the initial and additional data, finalizing with a numerical test.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
