Solutions in the large for the nonlinear hyperbolic conservation laws of gas dynamics
dc.contributor.author | Temple, J. Blake | en_US |
dc.date.accessioned | 2006-04-07T18:04:14Z | |
dc.date.available | 2006-04-07T18:04:14Z | |
dc.date.issued | 1981-07 | en_US |
dc.identifier.citation | Temple, J. Blake (1981/07)."Solutions in the large for the nonlinear hyperbolic conservation laws of gas dynamics." Journal of Differential Equations 41(1): 96-161. <http://hdl.handle.net/2027.42/24320> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6WJ2-4CX06GF-1H/2/7a762131a87510be8eb5e38b3c52b103 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/24320 | |
dc.description.abstract | The constraints under which a gas at a certain state will evolve can be given by three partial differential equations which express the conservation of momentum, mass, and energy. In these equations, a particular gas is defined by specifying the constitutive relation e = e(v, S), where e = specific internal energy, v = specific volume, and S = specific entropy. The energy function e = -1n v + (S/R) describes a polytropic gas for the exponent [gamma] = 1, and for this choice of e(V, S), global weak solutions for bounded measurable data having finite total variation were given by Nishida in [10]. Here the following general existence theorem is obtained: let e[epsilon](v, S) be any smooth one parameter family of energy functions such that at [var epsilon] = 0 the energy is given by e0(v, S) = - 1n v + (S/R). It is proven that there exists a constant C independent of [var epsilon], such that, if [var epsilon] [middle dot] (total variation of the initial data) C, then there exists a global weak solution to the equations. Since any energy function can be connected to [var epsilon]0(V, S) by a smooth parameterization, our results give an existence theorem for all the conservation laws of gas dynamics. As a corollary we obtain an existence theorem of Liu, [5.] for polytropic gases. The main point in this argument is that the nonlinear functional used to make the Glimm Scheme converge, depends only on properties of the equations at [var epsilon] = 0. For general n x n systems of conservation laws, this technique provides an alternate proof for the interaction estimates in Glimm's 1965 paper. The new result here is that certain interaction differences are bounded by [var epsilon] as well as by the approaching waves. | en_US |
dc.format.extent | 2822223 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | Solutions in the large for the nonlinear hyperbolic conservation laws of gas dynamics | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48104, USA | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/24320/1/0000587.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0022-0396(81)90055-3 | en_US |
dc.identifier.source | Journal of Differential Equations | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.