In this paper, we consider a coupled system of two biharmonic equations
with damping and source terms of variable-exponents nonlinearities,
supplemented with initial and mixed boundary conditions. We establish an
existence and uniqueness result of a weak solution, under suitable
assumptions on the variable exponents. Then, we show that solutions with
negative-initial energy blow up in finite time. To illustrate our
theoritical findings, we present two numerical examples.