BLOW UP FOR POSITIVE-INITIAL ENERGY AND DECAY OF A BIHARMONIC SYSTEM WITH VARIABLE-EXPONENT NONLINEARITIES

Abstract

This work is concerned with a coupled system of two biharmonic equations with variable exponents in the damping and source terms. Using the energy approach and for certain solution with positive initial data, we prove the blow-up theorem. Then, we establish the global existence as well as energy decay results of solutions, under appropriate conditions on the parameters of the problem, using the stable-set and the multiplier methods.