Singular properties of solutions for a parabolic equation with variable exponents and logarithmic source

Abstract This paper deals with a parabolic p ( x ) -Laplace equation with logarithmic source u q ( x ) log u . The singular properties of solutions are determined completely by classifying the initial energy. Moreover, we obtain a new extinction rate of solutions, where the order of the extinction rate is greater than the maximum of variable exponent q ( x ) . This kind of extinction rate could reflect the influence of logarithmic functions on the extinction of solutions more reasonably.