Global Existence of Classical Solutions to the Cauchy Problem on a Semi-bounded Initial Axis for Inhomogeneous Quaslinear Hyperbolic Systems

Journal Home
Volume 37 - 2024
- Vol. 37, Issue 1 pp.1-120
Volume 36 - 2023
- Vol. 36, Issue 4 pp.331-453
- Vol. 36, Issue 3 pp.235-330
- Vol. 36, Issue 2 pp.119-234
- Vol. 36, Issue 1 pp.1-118
Volume 35 - 2022
- Vol. 35, Issue 4 pp.307-408
- Vol. 35, Issue 3 pp.199-306
- Vol. 35, Issue 2 pp.101-198
- Vol. 35, Issue 1 pp.1-100
Volume 34 - 2021
- Vol. 34, Issue 4 pp.297-392
- Vol. 34, Issue 3 pp.201-296
- Vol. 34, Issue 2 pp.103-200
- Vol. 34, Issue 1 pp.1-102
Volume 33 - 2020
- Vol. 33, Issue 4 pp.291-394
- Vol. 33, Issue 3 pp.193-290
- Vol. 33, Issue 2 pp.93-192
- Vol. 33, Issue 1 pp.1-92
Volume 32 - 2019
- Vol. 32, Issue 4 pp.293-380
- Vol. 32, Issue 3 pp.191-292
- Vol. 32, Issue 2 pp.93-190
- Vol. 32, Issue 1 pp.1-92
Volume 31 - 2018
- Vol. 31, Issue 4 pp.291-384
- Vol. 31, Issue 3 pp.193-290
- Vol. 31, Issue 2 pp.97-192
- Vol. 31, Issue 1 pp.1-96
Volume 30 - 2017
- Vol. 30, Issue 4 pp.281-380
- Vol. 30, Issue 3 pp.189-280
- Vol. 30, Issue 2 pp.95-188
- Vol. 30, Issue 1 pp.1-94
Volume 29 - 2016
- Vol. 29, Issue 4 pp.255-359
- Vol. 29, Issue 3 pp.161-254
- Vol. 29, Issue 2 pp.89-160
- Vol. 29, Issue 1 pp.1-88
Volume 28 - 2015
- Vol. 28, Issue 4 pp.291-382
- Vol. 28, Issue 3 pp.197-290
- Vol. 28, Issue 2 pp.95-196
- Vol. 28, Issue 1 pp.1-94
Volume 27 - 2014
- Vol. 27, Issue 4 pp.283-372
- Vol. 27, Issue 3 pp.189-282
- Vol. 27, Issue 2 pp.95-188
- Vol. 27, Issue 1 pp.1-94
Volume 26 - 2013
- Vol. 26, Issue 4 pp.289-385
- Vol. 26, Issue 3 pp.193-288
- Vol. 26, Issue 2 pp.99-192
- Vol. 26, Issue 1 pp.1-98
Volume 25 - 2012
- Vol. 25, Issue 4 pp.295-387
- Vol. 25, Issue 3 pp.199-294
- Vol. 25, Issue 2 pp.103-198
- Vol. 25, Issue 1 pp.1-102
Volume 24 - 2011
- Vol. 24, Issue 4 pp.289-385
- Vol. 24, Issue 3 pp.195-288
- Vol. 24, Issue 2 pp.97-194
- Vol. 24, Issue 1 pp.1-96
Volume 23 - 2010
- Vol. 23, Issue 4 pp.305-401
- Vol. 23, Issue 3 pp.209-304
- Vol. 23, Issue 2 pp.105-208
- Vol. 23, Issue 1 pp.1-104
Volume 22 - 2009
- Vol. 22, Issue 4 pp.299-393
- Vol. 22, Issue 3 pp.199-298
- Vol. 22, Issue 2 pp.97-198
- Vol. 22, Issue 1 pp.1-96
Volume 21 - 2008
- Vol. 21, Issue 4 pp.289-383
- Vol. 21, Issue 3 pp.193-288
- Vol. 21, Issue 2 pp.97-192
- Vol. 21, Issue 1 pp.1-96
Volume 20 - 2007
- Vol. 20, Issue 4 pp.289-384
- Vol. 20, Issue 3 pp.193-288
- Vol. 20, Issue 2 pp.97-192
- Vol. 20, Issue 1 pp.1-96
Volume 19 - 2006
- Vol. 19, Issue 4 pp.289-383
- Vol. 19, Issue 3 pp.193-288
- Vol. 19, Issue 2 pp.97-192
- Vol. 19, Issue 1 pp.1-96
Volume 18 - 2005
- Vol. 18, Issue 4 pp.289-383
- Vol. 18, Issue 3 pp.193-288
- Vol. 18, Issue 2 pp.97-192
- Vol. 18, Issue 1 pp.1-96
Volume 17 - 2004
- Vol. 17, Issue 4 pp.289-383
- Vol. 17, Issue 3 pp.193-288
- Vol. 17, Issue 2 pp.97-192
- Vol. 17, Issue 1 pp.1-96
Volume 16 - 2003
- Vol. 16, Issue 4 pp.289-383
- Vol. 16, Issue 3 pp.193-288
- Vol. 16, Issue 2 pp.97-192
- Vol. 16, Issue 1 pp.1-96
Volume 15 - 2002
- Vol. 15, Issue 4 pp.1-95
- Vol. 15, Issue 3 pp.1-80
- Vol. 15, Issue 2 pp.1-96
- Vol. 15, Issue 1 pp.1-96
Volume 14 - 2001
- Vol. 14, Issue 4 pp.289-383
- Vol. 14, Issue 3 pp.193-288
- Vol. 14, Issue 2 pp.97-192
- Vol. 14, Issue 1 pp.1-96
Volume 13 - 2000
- Vol. 13, Issue 4 pp.289-383
- Vol. 13, Issue 3 pp.193-288
- Vol. 13, Issue 2 pp.97-192
- Vol. 13, Issue 1 pp.1-96
Volume 12 - 1999
- Vol. 12, Issue 4 pp.289-383
- Vol. 12, Issue 3 pp.193-288
- Vol. 12, Issue 2 pp.97-192
- Vol. 12, Issue 1 pp.1-96
Volume 11 - 1998
- Vol. 11, Issue 4 pp.289-383
- Vol. 11, Issue 3 pp.193-288
- Vol. 11, Issue 2 pp.97-192
- Vol. 11, Issue 1 pp.1-96
Volume 10 - 1997
- Vol. 10, Issue 4 pp.289-383
- Vol. 10, Issue 3 pp.193-288
- Vol. 10, Issue 2 pp.97-192
- Vol. 10, Issue 1 pp.1-96
Volume 9 - 1996
- Vol. 9, Issue 4 pp.289-383
- Vol. 9, Issue 3 pp.193-288
- Vol. 9, Issue 2 pp.97-192
- Vol. 9, Issue 1 pp.1-96
Volume 8 - 1995
- Vol. 8, Issue 4 pp.289-383
- Vol. 8, Issue 3 pp.193-288
- Vol. 8, Issue 2 pp.97-192
- Vol. 8, Issue 1 pp.1-96
Volume 7 - 1994
- Vol. 7, Issue 4 pp.289-383
- Vol. 7, Issue 3 pp.193-288
- Vol. 7, Issue 2 pp.97-192
- Vol. 7, Issue 1 pp.1-96
Volume 6 - 1993
- Vol. 6, Issue 4 pp.289-384
- Vol. 6, Issue 3 pp.193-288
- Vol. 6, Issue 2 pp.97-192
- Vol. 6, Issue 1 pp.1-96
Volume 5 - 1992
- Vol. 5, Issue 4 pp.1-95
- Vol. 5, Issue 3 pp.1-96
- Vol. 5, Issue 2 pp.1-96
- Vol. 5, Issue 1 pp.1-96
Volume 4 - 1991
- Vol. 4, Issue 4 pp.1-96
- Vol. 4, Issue 3 pp.1-96
- Vol. 4, Issue 2 pp.1-96
- Vol. 4, Issue 1 pp.1-96
Volume 3 - 1990
- Vol. 3, Issue 4 pp.1-95
- Vol. 3, Issue 3 pp.1-96
- Vol. 3, Issue 2 pp.1-96
- Vol. 3, Issue 1 pp.1-96
Volume 2 - 1989
- Vol. 2, Issue 4 pp.1-95
- Vol. 2, Issue 3 pp.1-96
- Vol. 2, Issue 2 pp.1-96
- Vol. 2, Issue 1 pp.1-94
Volume 1 - 1988
- Vol. 1, Issue 2 pp.1-96
- Vol. 1, Issue 1 pp.1-95

Volume 20, Issue 3

Weiwei Han

J. Part. Diff. Eq., 20 (2007), pp. 273-288.

Published online: 2007-08

Preview Purchase PDF 924 24947

Cited by

google scholar semantic scholar

Export citation

Abstract

In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost (resp. leftmost) eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C¹ solution with small and decaying initial data.

Keywords

Inhomogeneous quasilinear hyperbolic system Cauchy problem global classical solution weak linear degeneracy matching condition

AMS Subject Headings

35L45 35L60.

Email address

BibTex
RIS
TXT

@Article{JPDE-20-273, author = {}, title = {Global Existence of Classical Solutions to the Cauchy Problem on a Semi-bounded Initial Axis for Inhomogeneous Quaslinear Hyperbolic Systems}, journal = {Journal of Partial Differential Equations}, year = {2007}, volume = {20}, number = {3}, pages = {273--288}, abstract = { In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost (resp. leftmost) eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C¹ solution with small and decaying initial data.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5308.html} }

TY - JOUR T1 - Global Existence of Classical Solutions to the Cauchy Problem on a Semi-bounded Initial Axis for Inhomogeneous Quaslinear Hyperbolic Systems JO - Journal of Partial Differential Equations VL - 3 SP - 273 EP - 288 PY - 2007 DA - 2007/08 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5308.html KW - Inhomogeneous quasilinear hyperbolic system KW - Cauchy problem KW - global classical solution KW - weak linear degeneracy KW - matching condition AB - In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost (resp. leftmost) eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C¹ solution with small and decaying initial data.

Weiwei Han . (2019). Global Existence of Classical Solutions to the Cauchy Problem on a Semi-bounded Initial Axis for Inhomogeneous Quaslinear Hyperbolic Systems. Journal of Partial Differential Equations. 20 (3). 273-288. doi:

Copy to clipboard

BibteX RIS TXT

The citation has been copied to your clipboard

- LOGIN -

- E-mail verification -

- REGISTER -