Approximation of nonlinear wave equations with nonstandard anisotropic growth conditions

Weak solutions for nonlinear wave equations involving the p(x)-Laplacian, for p : (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 criterion 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 blow-up, and asymptotic decay behavior.

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Jonas Haehnle, Andreas Prohl
• Keywords: Appropriate Stopping Criterion, Finite Element Discretization, MOC 2010, Nonlinear Wave Equations, Security Privacy