This paper addresses the questions of well-posedness to fractional m-Laplacian reaction diffusion equation with singular potential term and logarithmic nonlinearity:

where \(R(u)=\left| u\right| ^{r}\ln (|u|)\). Guided by the made assumptions, we arrive at the conclusions of the local and global solvability of solutions within the framework of Galerkin approximation. In addition, this study considers weak solutions’ asymptotic stability and explosion in finite time. Significantly, we not only figure out the relationship between the non-local fractional operator and singular potential term, but generalize and improve earlier results in the literature.

本文解决了具有奇异势项和对数非线性的分数阶 m-Laplacian 反应扩散方程的适定性问题：

其中 \（R（u）=\left| u\right| ^{r}\ln （|u|）\） 的在所做假设的指导下，我们在 Galerkin 近似的框架内得出了解的局部和全局可解性的结论。此外，本研究还考虑了弱解在有限时间内的渐近稳定性和爆炸。值得注意的是，我们不仅弄清楚了非局部分数运算符和奇异潜在项之间的关系，而且推广和改进了文献中的早期结果。