Title: The existence of a global weak solution to the non‐linear waterhammer problem
Abstract: Communications on Pure and Applied MathematicsVolume 35, Issue 5 p. 697-735 Article The existence of a global weak solution to the non-linear waterhammer problem Mitchell Luskin, Mitchell Luskin University of MinnesotaSearch for more papers by this authorBlake Temple, Blake Temple The Rockefeller UniversitySearch for more papers by this author Mitchell Luskin, Mitchell Luskin University of MinnesotaSearch for more papers by this authorBlake Temple, Blake Temple The Rockefeller UniversitySearch for more papers by this author First published: September 1982 https://doi.org/10.1002/cpa.3160350505Citations: 51AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Bibliography 1 Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18, 1965, pp. 697–715. 10.1002/cpa.3160180408 Web of Science®Google Scholar 2 Glimm, J., and Lax, P. D., Decay of solutions of systems of nonlinear hyperbolic conservation laws, Mem. Amer. Math. Soc. 101, 1970. Google Scholar 3 Lax, P. D., Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10, 1957, pp. 537–566. 10.1002/cpa.3160100406 Web of Science®Google Scholar 4 Lax, P. D., Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Math. Phys. 5, 1964, pp. 611–613. 10.1063/1.1704154 Web of Science®Google Scholar 5 Liu, T.-P., Initial-boundary value problems of gas dynamics, Arch. Rational Mech. Anal. 64, 1977, pp. 137–168. 10.1007/BF00280095 Web of Science®Google Scholar 6 Liu, T.-P., Quasilinear hyperbolic systems, Comm. Math. Phys. 68, 1979, pp. 141–172. 10.1007/BF01418125 Web of Science®Google Scholar 7 Luskin, M., On the existence of global smooth solutions for a model equation for fluid flow in a pipe, J. Math. Anal. Appl., 84, 1981, pp. 614–630. 10.1016/0022-247X(81)90192-X Web of Science®Google Scholar 8 Marchesin, D., and Paes-Leme, P. J., Shocks in gas pipelines, preprint. Google Scholar 9 Nishida, T., Global solution for an initial boundary value problem of a quasilinear hyperbolic system, Proc. Jap. Acad. 44, 1968, pp. 642–646. 10.3792/pja/1195521083 Web of Science®Google Scholar 10 Nishida, T., and Smoller, J., Solutions in the large for some nonlinear hyperbolic conservation laws, Comm. Pure Appl. Math. 26, 1973, pp. 183–200. 10.1002/cpa.3160260205 Web of Science®Google Scholar 11 Nishida, T., and Smoller, J., Mixed problems for nonlinear conservation laws, J. Differential Eq. 23, 1977, pp. 244–269. 10.1016/0022-0396(77)90129-2 Web of Science®Google Scholar 12 Streeter, V., and Wylie, E. B., Fluid Mechanics, 6th ed., McGraw-Hill, New York, 1975. Google Scholar 13 Temple, B., Solutions in the large for the nonlinear hyperbolic conservation laws of gas dynamics, J. Differential Eq., 41, 1981, pp. 96–161. 10.1016/0022-0396(81)90055-3 Web of Science®Google Scholar 14 Ying, L.-A., and Wang, C.-H., Global solutions of the Cauchy problem for a nonhomogeneous quasilinear hyperbolic system, Comm. Pure Appl. Math. 33, 1980, pp. 579–597. 10.1002/cpa.3160330502 Web of Science®Google Scholar Citing Literature Volume35, Issue5September 1982Pages 697-735 ReferencesRelatedInformation
Publication Year: 1982
Publication Date: 1982-09-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 63
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