Asymptotic Estimates and Fujita Exponents of Blow-Up Solutions in Weighted Parabolic Systems

In this paper, we consider the time-weighted parabolic equations in a bounded domain, subject to homogeneous Dirichlet boundary conditions. First, we determine the critical Fujita exponents of solutions prescribed by the coefficients of weighted functions and the first eigenvalue of Laplacian operator with zero Dirichlet boundary. Second, we distinguish completely simultaneous blow-up from non-simultaneous blow-up of two components of solutions. Third, blow-up rates and blow-up time estimates are studied according to different blow-up phenomena. It can be found out that the nonlinear functions of the components determine the orders of them.