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This paper concerns the singularity and global regularity for the porous medium equation with time-dependent coefficients under homogeneous Dirichlet boundary conditions. Firstly, some global regularity results are established. Furthermore, we investigate the blow-up solution to the boundary value problem. The upper and lower estimates to the lifespan of the singular solution are also obtained here.

Singularity Analysis for a Class of Porous Medium Equation with Time-Dependent Coefficients