Abstract: This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions. We give the blow-up criteria for all nonnegative nontrivial solutions, which rely on the behavior of the coefficients when time variable tends to positive infinity. Moreover, the global existence of solutions are discussed for non-positive exponents.

Key words: Semilinear parabolic equation, Nonlinear memory boundary flux, Variable , coefficient, Blow-up