A class of parabolic equations with combined logarithmic nonlinearities

In this talk, we focus on a class of parabolic equations with combined logarithmic nonlinearities. By employing the key ingredients of modified potential well method, we obtain the existence of a global weak solution and the phenomenon of finite-time blow-up. We show that the global weak solution exhibits exponential decay. Our analysis reveals that the higher-order power term in the combined logarithmic nonlinearities dominates the blow-up behavior of solutions. Furthermore, we derive both an upper and a lower bound for the blow-up time.