The article deals with the existence of solutions of an integro-differential equation in the case of anomalous diffusion with the negative Laplace operator in a fractional power in the presence of the transport term. The proof of existence of solutions is based on a fixed point technique. Solvability conditions for elliptic operators without the Fredholm property in unbounded domains are used. We discuss how the introduction of the transport term impacts the regularity of solutions.

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一些具有异常扩散和输运的积分微分方程的可解性

这篇文章讨论了在反常扩散的情况下积分微分方程解的存在性，在存在输运项的情况下，负拉普拉斯算子在分数幂中。解存在性的证明基于不动点技术。使用无界域中没有 Fredholm 性质的椭圆算子的可解性条件。我们讨论传输项的引入如何影响解决方案的规律性。