• Previous Article
    Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
  • PROC Home
  • This Issue
  • Next Article
    A long-time stable fully discrete approximation of the Cahn-Hilliard equation with inertial term
2011, 2011(Special): 533-542. doi: 10.3934/proc.2011.2011.533

Cauchy problem for a class of nondiagonalizable hyperbolic systems

1. 

Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy, Italy

Received  July 2010 Revised  March 2011 Published  October 2011

We investigate the well-posedness of Cauchy problem for weakly hyperbolic systems in one space dimension with time dependent coecients in Sobolev spaces and in the $C^\infty$ category allowing nondiagonalizable principal parts and complex entries in the nilpotent part. We prove well-posedness results by means of an iterative approach under conditions linking the characteristic roots, the entries of the nilpotent part and of the zero order part.
Citation: Todor Gramchev, Nicola Orrú. Cauchy problem for a class of nondiagonalizable hyperbolic systems. Conference Publications, 2011, 2011 (Special) : 533-542. doi: 10.3934/proc.2011.2011.533
[1]

Cunming Liu, Jianli Liu. Stability of traveling wave solutions to Cauchy problem of diagnolizable quasilinear hyperbolic systems. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4735-4749. doi: 10.3934/dcds.2014.34.4735

[2]

Libin Wang. Breakdown of $C^1$ solution to the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Communications on Pure & Applied Analysis, 2003, 2 (1) : 77-89. doi: 10.3934/cpaa.2003.2.77

[3]

Viorel Niţică. Stable transitivity for extensions of hyperbolic systems by semidirect products of compact and nilpotent Lie groups. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 1197-1204. doi: 10.3934/dcds.2011.29.1197

[4]

Michel H. Geoffroy, Alain Piétrus. A fast iterative scheme for variational inclusions. Conference Publications, 2009, 2009 (Special) : 250-258. doi: 10.3934/proc.2009.2009.250

[5]

V. Varlamov, Yue Liu. Cauchy problem for the Ostrovsky equation. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 731-753. doi: 10.3934/dcds.2004.10.731

[6]

Mauro Garavello, Paola Goatin. The Cauchy problem at a node with buffer. Discrete & Continuous Dynamical Systems - A, 2012, 32 (6) : 1915-1938. doi: 10.3934/dcds.2012.32.1915

[7]

Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial & Management Optimization, 2008, 4 (1) : 1-15. doi: 10.3934/jimo.2008.4.1

[8]

Morten Brøns. An iterative method for the canard explosion in general planar systems. Conference Publications, 2013, 2013 (special) : 77-83. doi: 10.3934/proc.2013.2013.77

[9]

Petr Kůrka. Minimality in iterative systems of Möbius transformations. Conference Publications, 2011, 2011 (Special) : 903-912. doi: 10.3934/proc.2011.2011.903

[10]

Petr Kůrka. Iterative systems of real Möbius transformations. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 567-574. doi: 10.3934/dcds.2009.25.567

[11]

Zhan-Dong Mei, Jigen Peng, Yang Zhang. On general fractional abstract Cauchy problem. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2753-2772. doi: 10.3934/cpaa.2013.12.2753

[12]

Rudong Zheng, Zhaoyang Yin. The Cauchy problem for a generalized Novikov equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3503-3519. doi: 10.3934/dcds.2017149

[13]

Sören Bartels, Marijo Milicevic. Iterative finite element solution of a constrained total variation regularized model problem. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1207-1232. doi: 10.3934/dcdss.2017066

[14]

Arturo de Pablo, Guillermo Reyes, Ariel Sánchez. The Cauchy problem for a nonhomogeneous heat equation with reaction. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 643-662. doi: 10.3934/dcds.2013.33.643

[15]

Felipe Linares, M. Panthee. On the Cauchy problem for a coupled system of KdV equations. Communications on Pure & Applied Analysis, 2004, 3 (3) : 417-431. doi: 10.3934/cpaa.2004.3.417

[16]

Belkacem Said-Houari, Salim A. Messaoudi. General decay estimates for a Cauchy viscoelastic wave problem. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1541-1551. doi: 10.3934/cpaa.2014.13.1541

[17]

Hernan R. Henriquez. Generalized solutions for the abstract singular Cauchy problem. Communications on Pure & Applied Analysis, 2009, 8 (3) : 955-976. doi: 10.3934/cpaa.2009.8.955

[18]

Guillermo Reyes, Juan-Luis Vázquez. The Cauchy problem for the inhomogeneous porous medium equation. Networks & Heterogeneous Media, 2006, 1 (2) : 337-351. doi: 10.3934/nhm.2006.1.337

[19]

Shaoyong Lai, Yong Hong Wu. The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 401-408. doi: 10.3934/dcdsb.2003.3.401

[20]

Binhua Feng, Xiangxia Yuan. On the Cauchy problem for the Schrödinger-Hartree equation. Evolution Equations & Control Theory, 2015, 4 (4) : 431-445. doi: 10.3934/eect.2015.4.431

 Impact Factor: 

Metrics

  • PDF downloads (2)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]