Blow-up solutions and numerical simulation for a class of quasilinear parabolic equations

This paper mainly studies quasilinear parabolic equations with gradient terms and space-time-dependent coefficients under Robin boundary conditions. By constructing auxiliary functions and combining modified differential inequalities, we prove that the solution will blow up under some appropriate assumptions, and provide upper and lower bounds of the blow up time. We also prove the conditions for the existence of global solutions. This indicates that by imposing different constraints on the function, it is possible to control whether the solution blow-up. Finally, an example is given and the main conclusions are verified by numerical simulation.