Approximation of nonlinear wave equations with nonstandard anisotropic growth conditions

Weak solutions for nonlinear wave equations involving the p(x)Laplacian, for p : Ω → (1,∞) are constructed as appropriate limits of solutions of an implicit finite element discretization of the problem. A simple fixed-point scheme with appropriate stopping criteria is proposed to conclude convergence for all discretization, regularization, perturbation, and stopping parameters tending to zero. Computational experiments are included to motivate interesting dynamics, such as blowup, and asymptotic decay behavior.