Some degenerate and generalized wave models in elasto- and hydrodynamics

✍ Scribed by I.T Selezov

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 524 KB
• Volume: 67
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(03)90508-9

✦ Synopsis

Models, degenerate with respect to a small parameter, which describe the propagation of disturbances with a finite velocity, are considered. Example, when parabolic models degenerate into hyperbolic ones and, inversely, when hyperbolic models can be obtained by a generalization of parabolic models, are given. The reduction of the three-dimensional problem of elasto-dynamics for a layer to a two-dimensional one on the basis of power series, and also the construction of weakly dispersive, but strongly non-linear models of the propagation of surface waves on water, close to hyperbolic models, are considered in more detail.