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Blow-up and Global Solutions for a Porous Medium Equation Under Robin Boundary Conditions

This paper deals with blow-up and global solutions for a porous medium equation under Robin boundary conditions. By constructing auxiliary functions and using modified differential inequality techniques, we establish conditions to ensure that the solution blows up in some finite time or remains global. Moreover, an upper and a lower bound for blow-up time are derived. Finally, an example is given to illustrate the applications of obtained results.