Local and global well-posedness of semilinear Reissner–Mindlin–Timoshenko plate equations

This is a study of local and global well-posedness of nonlinearly perturbed Reissner–Mindlin–Timoshenko plate equations. This PDE system represents an extension of the Timoshenko beam model to plates and accounts for shear deformations. The primary feature of the considered model is the interplay between nonlinear viscous interior damping and nonlinear source terms. The main results verify local and global existence of solutions as well as their continuous dependence on the initial data in the appropriate function spaces. Moreover, a blow-up result is proved for solutions with negative initial energy.