Global existence, asymptotic stability and blow up of solutions for a nonlinear viscoelastic plate equation involving (p(x); q(x))-Laplacian operator

This study aims at investigating the global existence, asymptotic stability and blow up of solutions for a nonlinear viscoelastic fourth-order (p(x), q(x))-Laplacian equation with variable -exponent nonlinearities. First, we prove the global existence of solutions, and next, we show that the solutions are asymptotically stable if initial data p(x) and q(x) are in the appropriate range. Moreover, under suitable conditions on initial data, we prove that there exists a finite time in which some solutions blow up with positive as well as negative initial energies.