Singularity Formation in Systems of Non-strictly Hyperbolic Equations
dc.contributor.author | Saxton, R. | |
dc.contributor.author | Vinod, V. | |
dc.date.accessioned | 2018-08-23T14:55:27Z | |
dc.date.available | 2018-08-23T14:55:27Z | |
dc.date.issued | 1995-06-28 | |
dc.description.abstract | We analyze finite time singularity formation for two systems of hyperbolic equations. Our results extend previous proofs of breakdown concerning 2 × 2 non-strictly hyperbolic systems to n × n systems, and to a situation where, additionally, the condition of genuine nonlinearity is violated throughout phase space. The systems we consider include as special cases those examined by Keyfitz and Kranzer and by Serre. They take the form ut + (ϕ(u)u)x = 0, where ϕ is a scalar-valued function of the n-dimensional vector u, and ut + Λ(u)ux = 0, under the assumption Λ = diag {λ1,..., λn} with λi = λi(u − ui), where u − ui ≡ {u1,..., ui−1, ui+1,..., un}. | |
dc.description.department | Mathematics | |
dc.format | Text | |
dc.format.extent | 15 pages | |
dc.format.medium | 1 file (.pdf) | |
dc.identifier.citation | Saxton, R. & Vinod, V. (1995). Singularity formation in systems of non-strictly hyperbolic equations. Electronic Journal of Differential Equations, 1995(09), pp. 1-15. | |
dc.identifier.issn | 1072-6691 | |
dc.identifier.uri | https://hdl.handle.net/10877/7589 | |
dc.language.iso | en | |
dc.publisher | Southwest Texas State University, Department of Mathematics | |
dc.rights | Attribution 4.0 International | |
dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.source | Electronic Journal of Differential Equations, 1995, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
dc.subject | finite time breakdown | |
dc.subject | non-strict hyperbolicity | |
dc.subject | linear degeneracy | |
dc.title | Singularity Formation in Systems of Non-strictly Hyperbolic Equations | |
dc.type | Article |