Analysis of large time asymptotics of the fourth‐order parabolic system involving variable coefficients and mixed nonlinearities

Abstract

In a general domain, we discuss an initial value problem for the symmetry generalized ‐coupled system of fourth‐order parabolic equations with space–time‐dependent diffusion coefficients and mixed nonlinearities. For the power‐type nonlinearities containing the sub‐critical Sobolev exponents, we achieve the local existence, a unique continuation, global existence, or finite‐time blow‐up of solutions to the system in time‐weighted Sobolev space. For the logarithmic nonlinearities containing the critical Sobolev exponents, we investigate the local existence in time‐weighted Sobolev space.