American Institute of Mathematical Sciences

Advanced
January  2004, 11(1): 205-220. doi: 10.3934/dcds.2004.11.205

Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems

G. Métivier 1, and  K. Zumbrun 2,

1. 

MAB, Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex
2. 

Mathematics Department, Indiana University, Bloomington, IN 47405

Received  December 2002 Revised  November 2003 Published  April 2004

In this paper we prove the continuity of stable subspaces associated to parabolic-hyperbolic boundary value problems, for limiting values of parameters. The analysis is based on the construction performed in [MZ] of Kreiss' type symmetrizers.
Keywords: Lopatinski determinant and Evans functions, Hyperbolic and parabolic boundary value problems, plane wave stability, positive and negative stable subspaces., Kreiss symmetrizers.
Mathematics Subject Classification: 35K50, 35L50, 35L6.
Citation: G. Métivier, K. Zumbrun. Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems. Discrete & Continuous Dynamical Systems, 2004, 11 (1) : 205-220. doi: 10.3934/dcds.2004.11.205
[1]

Genni Fragnelli, Dimitri Mugnai. Stability of solutions for nonlinear wave equations with a positive--negative damping. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 615-622. doi: 10.3934/dcdss.2011.4.615
[2]

Hugo Beirão da Veiga. Elliptic boundary value problems in spaces of continuous functions. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 43-52. doi: 10.3934/dcdss.2016.9.43
[3]

G. Infante. Positive solutions of nonlocal boundary value problems with singularities. Conference Publications, 2009, 2009 (Special) : 377-384. doi: 10.3934/proc.2009.2009.377
[4]

John R. Graef, Lingju Kong, Qingkai Kong, Min Wang. Positive solutions of nonlocal fractional boundary value problems. Conference Publications, 2013, 2013 (special) : 283-290. doi: 10.3934/proc.2013.2013.283
[5]

John V. Baxley, Philip T. Carroll. Nonlinear boundary value problems with multiple positive solutions. Conference Publications, 2003, 2003 (Special) : 83-90. doi: 10.3934/proc.2003.2003.83
[6]

Laurence Halpern, Jeffrey Rauch. Hyperbolic boundary value problems with trihedral corners. Discrete & Continuous Dynamical Systems, 2016, 36 (8) : 4403-4450. doi: 10.3934/dcds.2016.36.4403
[7]

Sofia Giuffrè, Giovanna Idone. On linear and nonlinear elliptic boundary value problems in the plane with discontinuous coefficients. Discrete & Continuous Dynamical Systems, 2011, 31 (4) : 1347-1363. doi: 10.3934/dcds.2011.31.1347
[8]

Shiping Cao, Hua Qiu. Boundary value problems for harmonic functions on domains in Sierpinski gaskets. Communications on Pure & Applied Analysis, 2020, 19 (2) : 1147-1179. doi: 10.3934/cpaa.2020054
[9]

J. R. L. Webb. Remarks on positive solutions of some three point boundary value problems. Conference Publications, 2003, 2003 (Special) : 905-915. doi: 10.3934/proc.2003.2003.905
[10]

K. Q. Lan. Multiple positive eigenvalues of conjugate boundary value problems with singularities. Conference Publications, 2003, 2003 (Special) : 501-506. doi: 10.3934/proc.2003.2003.501
[11]

M. Gaudenzi, P. Habets, F. Zanolin. Positive solutions of superlinear boundary value problems with singular indefinite weight. Communications on Pure & Applied Analysis, 2003, 2 (3) : 411-423. doi: 10.3934/cpaa.2003.2.411
[12]

Wenying Feng. Solutions and positive solutions for some three-point boundary value problems. Conference Publications, 2003, 2003 (Special) : 263-272. doi: 10.3934/proc.2003.2003.263
[13]

Nicola Abatangelo, Sven Jarohs, Alberto Saldaña. Positive powers of the Laplacian: From hypersingular integrals to boundary value problems. Communications on Pure & Applied Analysis, 2018, 17 (3) : 899-922. doi: 10.3934/cpaa.2018045
[14]

Matthias Eller, Daniel Toundykov. Carleman estimates for elliptic boundary value problems with applications to the stablization of hyperbolic systems. Evolution Equations & Control Theory, 2012, 1 (2) : 271-296. doi: 10.3934/eect.2012.1.271
[15]

Aimin Huang, Roger Temam. The linear hyperbolic initial and boundary value problems in a domain with corners. Discrete & Continuous Dynamical Systems - B, 2014, 19 (6) : 1627-1665. doi: 10.3934/dcdsb.2014.19.1627
[16]

Mark I. Vishik, Sergey Zelik. Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit. Communications on Pure & Applied Analysis, 2014, 13 (5) : 2059-2093. doi: 10.3934/cpaa.2014.13.2059
[17]

Hiroshi Watanabe. Solvability of boundary value problems for strongly degenerate parabolic equations with discontinuous coefficients. Discrete & Continuous Dynamical Systems - S, 2014, 7 (1) : 177-189. doi: 10.3934/dcdss.2014.7.177
[18]

Jerry L. Bona, Hongqiu Chen, Shu-Ming Sun, Bing-Yu Zhang. Comparison of quarter-plane and two-point boundary value problems: The KdV-equation. Discrete & Continuous Dynamical Systems - B, 2007, 7 (3) : 465-495. doi: 10.3934/dcdsb.2007.7.465
[19]

Jerry Bona, Hongqiu Chen, Shu Ming Sun, B.-Y. Zhang. Comparison of quarter-plane and two-point boundary value problems: the BBM-equation. Discrete & Continuous Dynamical Systems, 2005, 13 (4) : 921-940. doi: 10.3934/dcds.2005.13.921
[20]

V. A. Dougalis, D. E. Mitsotakis, J.-C. Saut. On initial-boundary value problems for a Boussinesq system of BBM-BBM type in a plane domain. Discrete & Continuous Dynamical Systems, 2009, 23 (4) : 1191-1204. doi: 10.3934/dcds.2009.23.1191

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (67)
  • HTML views (0)
  • Cited by (8)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy