On a reaction-diffusion equation with a singular coefficient and a variable exponent source: global existence and blow-up time

The paper investigates an initial boundary value problem for a reaction-diffusion equation with a singular coefficient and a variable exponent source, which is present in various physical models. The study explores three initial energy levels: subcritical, critical, and supercritical. For the subcritical initial energy, we establish blow-up and we estimate the blow-up time from above and from below. For the critical initial energy, the research shows the global existence, asymptotic behavior, finite-time blow-up, and a lower bound of the blow-up time. Finally, for the supercritical initial energy, finite time blow-up and lower and upper estimates of the blow-up time are proven.