RT journal article
T1 Conservation laws and variational structure of damped nonlinear wave equations
A1 Anco, Stephen C.
A1 Márquez Lozano, Almudena del Pilar
A1 Garrido Letrán, Tamara María
A1 Gandarias Núñez, María Luz
A2 Matemáticas
K1 conservation laws
K1 conserved integrals
K1 damping
K1 energy
K1 momentum
K1 nonlinear wave equations
AB All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted much attention in analysis. The conservation laws describe generalized momentum and boost momentum, conformal momentum, generalized energy, dilational energy, and light cone energies. Both the conformal momentum and dilational energy have no counterparts for nonlinear undamped wave equations in one dimension. All of the conservation laws are obtainable through Noether's theorem, which is applicable because the damping term can be transformed into a time-dependent self-interaction term by a change of dependent variable. For several of the conservation laws, the corresponding variational symmetries have a novel form which is different than any of the well-known variational symmetries admitted by nonlinear undamped wave equations in one dimension.
PB Wiley
SN 0170-4214
YR 2023
FD 2023-11-27
LK http://hdl.handle.net/10498/31333
UL http://hdl.handle.net/10498/31333
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 21-sep-2026