Singularity Formation in Systems of Non-strictly Hyperbolic Equations
Date
1995-06-28
Authors
Saxton, R.
Vinod, V.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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}.
Description
Keywords
Finite time breakdown, Non-strict hyperbolicity, Linear degeneracy
Citation
Saxton, R. & Vinod, V. (1995). Singularity formation in systems of non-strictly hyperbolic equations. <i>Electronic Journal of Differential Equations, 1995</i>(09), pp. 1-15.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.