Abstract
We consider the linearized equations in the Lagrangian variables and the Lagrangian coordinates for the propagation of acoustic waves in two media which are separated by an interface in the phase space R{sup n}, n {>=} 2. We obtain hyperbolic systems with discontinuous coefficients and the interface is characteristic for the corresponding system. We show under certain conditions that for two fluids there exist continuous piecewise smooth solutions while for two elastic solids we give a necessary and sufficient condition via the Lame coefficients for the existence of such solutions. (author). 6 refs.
Gramchev, T
[1]
- Bulgarian Academy of Sciences, Sofia (Bulgaria). Inst. of Mathematics
Citation Formats
Gramchev, T.
Classical-solutions to singular hyperbolic systems modelling acoustic wave propagation.
IAEA: N. p.,
1994.
Web.
Gramchev, T.
Classical-solutions to singular hyperbolic systems modelling acoustic wave propagation.
IAEA.
Gramchev, T.
1994.
"Classical-solutions to singular hyperbolic systems modelling acoustic wave propagation."
IAEA.
@misc{etde_101434,
title = {Classical-solutions to singular hyperbolic systems modelling acoustic wave propagation}
author = {Gramchev, T}
abstractNote = {We consider the linearized equations in the Lagrangian variables and the Lagrangian coordinates for the propagation of acoustic waves in two media which are separated by an interface in the phase space R{sup n}, n {>=} 2. We obtain hyperbolic systems with discontinuous coefficients and the interface is characteristic for the corresponding system. We show under certain conditions that for two fluids there exist continuous piecewise smooth solutions while for two elastic solids we give a necessary and sufficient condition via the Lame coefficients for the existence of such solutions. (author). 6 refs.}
place = {IAEA}
year = {1994}
month = {Dec}
}
title = {Classical-solutions to singular hyperbolic systems modelling acoustic wave propagation}
author = {Gramchev, T}
abstractNote = {We consider the linearized equations in the Lagrangian variables and the Lagrangian coordinates for the propagation of acoustic waves in two media which are separated by an interface in the phase space R{sup n}, n {>=} 2. We obtain hyperbolic systems with discontinuous coefficients and the interface is characteristic for the corresponding system. We show under certain conditions that for two fluids there exist continuous piecewise smooth solutions while for two elastic solids we give a necessary and sufficient condition via the Lame coefficients for the existence of such solutions. (author). 6 refs.}
place = {IAEA}
year = {1994}
month = {Dec}
}