EXISTENCE OF GLOBAL SOLUTIONS AND BLOW-UP RESULTS FOR A CLASS OF p(x)−LAPLACIAN HEAT EQUATIONS WITH LOGARITHMIC NONLINEARITY

Abstract

Abstract. This paper’s main objective is to examine an initial boundary value problem of a quasilinear parabolic equation of non-standard growth and logarithmic nonlinearity by utilizing the logarithmic Sobolev inequality and potential well method. Results of global existence, estimates of polynomial decay, and blowing up of weak solutions have been obtained under certain conditions that will be stated later. Our results extend those of a recent paper that appeared in the literature.