Growth rates of total variations of snapshots of 1D linear wave equations with nonlinear right-end boundary conditions
The vibrations of the solution of the one dimensional homogeneous wave equation under initial and boundary conditions are studied. The left-end boundary condition is linear and the right-hand is nonlinear. By a traveling wave approach explicit expressions for the Riemann invariants \((u ,v)\) are computed. Results regarding the growth of the total variations of \(u(.,t)\) and \(v(.,t)\) are proved. At the end of the paper, applications of the stated results, followed by numerical simulations are shown.
scientific article; zbMATH DE number 5625387