Semi-linear wave equations with effective damping

Semi-linear wave equations

This survey reviews some of the recent work on semilinear wave equations, in particular the wave map equation. We discuss wellposedness, as well as the construction of special solutions and their stability. Mathematics Subject Classification (2010). 35L05, 35L52, 37K40, 37K45, 53Z05

Low Regularity Semi-linear Wave Equations

We prove local well-posedness results for the semi-linear wave equation for data in H , 0 < < n?3 2(n?1) , extending the previously known results for this problem. The improvement comes from an introduction of a two-scale Lebesgue space X r;p k .

Wave equations with non-dissipative damping

Se p 19 97 LOW REGULARITY SEMI - LINEAR WAVE EQUATIONS

We prove local well-posedness results for the semi-linear wave equation for data in H γ , 0 < γ < n−3 2(n−1) , extending the previously known results for this problem. The improvement comes from an introduction of a two-scale Lebesgue space X r,p k .

A Linear Difference Scheme for Dissipative Symmetric Regularized Long Wave Equations with Damping Term

We study the initial-boundary problem of dissipative symmetric regularized long wave equations with damping term by finite difference method. A linear three-level implicit finite difference scheme is designed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is of second-order convergence and unconditionally stable by the discrete energ...