# American Institute of Mathematical Sciences

January  1997, 3(1): 91-106. doi: 10.3934/dcds.1997.3.91

## On the global solvability of symmetric hyperbolic systems of Kirchhoff type

 1 Dipartimento di Costruzioni, Istituto Universitario di Architettura, Tolentini, S. Croce 191 - 30135 Venezia, Italy

Received  April 1996 Revised  July 1996 Published  October 1996

We shall prove here the global solvability for small initial data for symmetric hyperbolic systems with integro-differential coefficients. In this way, we will extend some results obtained in [5], [6], [8], [11] for the classic Kirchhoff equation and in [3] for regularly hyperbolic systems.
Citation: Renato Manfrin. On the global solvability of symmetric hyperbolic systems of Kirchhoff type. Discrete & Continuous Dynamical Systems, 1997, 3 (1) : 91-106. doi: 10.3934/dcds.1997.3.91
 [1] Manil T. Mohan, Sivaguru S. Sritharan. New methods for local solvability of quasilinear symmetric hyperbolic systems. Evolution Equations & Control Theory, 2016, 5 (2) : 273-302. doi: 10.3934/eect.2016005 [2] Zhiqing Liu, Zhong Bo Fang. Global solvability and general decay of a transmission problem for kirchhoff-type wave equations with nonlinear damping and delay term. Communications on Pure & Applied Analysis, 2020, 19 (2) : 941-966. doi: 10.3934/cpaa.2020043 [3] Cyril Joel Batkam, João R. Santos Júnior. Schrödinger-Kirchhoff-Poisson type systems. Communications on Pure & Applied Analysis, 2016, 15 (2) : 429-444. doi: 10.3934/cpaa.2016.15.429 [4] Wenguo Shen. Unilateral global interval bifurcation for Kirchhoff type problems and its applications. Communications on Pure & Applied Analysis, 2018, 17 (1) : 21-37. doi: 10.3934/cpaa.2018002 [5] Marina Ghisi, Massimo Gobbino. Hyperbolic--parabolic singular perturbation for mildly degenerate Kirchhoff equations: Global-in-time error estimates. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1313-1332. doi: 10.3934/cpaa.2009.8.1313 [6] Irena Pawłow, Wojciech M. Zajączkowski. The global solvability of a sixth order Cahn-Hilliard type equation via the Bäcklund transformation. Communications on Pure & Applied Analysis, 2014, 13 (2) : 859-880. doi: 10.3934/cpaa.2014.13.859 [7] Ken Shirakawa. Solvability for phase field systems of Penrose-Fife type associated with $p$-laplacian diffusions. Conference Publications, 2007, 2007 (Special) : 927-937. doi: 10.3934/proc.2007.2007.927 [8] Zheng Han, Daoyuan Fang. Almost global existence for the Klein-Gordon equation with the Kirchhoff-type nonlinearity. Communications on Pure & Applied Analysis, 2021, 20 (2) : 737-754. doi: 10.3934/cpaa.2020287 [9] Yongqiang Fu, Xiaoju Zhang. Global existence and asymptotic behavior of weak solutions for time-space fractional Kirchhoff-type diffusion equations. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021091 [10] Maoding Zhen, Binlin Zhang, Xiumei Han. A new approach to get solutions for Kirchhoff-type fractional Schrödinger systems involving critical exponents. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021115 [11] Hugo Beirão da Veiga, Francesca Crispo. On the global regularity for nonlinear systems of the $p$-Laplacian type. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1173-1191. doi: 10.3934/dcdss.2013.6.1173 [12] Michael Ruzhansky, Jens Wirth. Dispersive type estimates for fourier integrals and applications to hyperbolic systems. Conference Publications, 2011, 2011 (Special) : 1263-1270. doi: 10.3934/proc.2011.2011.1263 [13] Tohru Nakamura, Shinya Nishibata, Naoto Usami. Convergence rate of solutions towards the stationary solutions to symmetric hyperbolic-parabolic systems in half space. Kinetic & Related Models, 2018, 11 (4) : 757-793. doi: 10.3934/krm.2018031 [14] Jijiang Sun, Chun-Lei Tang. Resonance problems for Kirchhoff type equations. Discrete & Continuous Dynamical Systems, 2013, 33 (5) : 2139-2154. doi: 10.3934/dcds.2013.33.2139 [15] Yijing Sun, Yuxin Tan. Kirchhoff type equations with strong singularities. Communications on Pure & Applied Analysis, 2019, 18 (1) : 181-193. doi: 10.3934/cpaa.2019010 [16] Moritz Kassmann, Tadele Mengesha, James Scott. Solvability of nonlocal systems related to peridynamics. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1303-1332. doi: 10.3934/cpaa.2019063 [17] Tatsien Li (Daqian Li). Global exact boundary controllability for first order quasilinear hyperbolic systems. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1419-1432. doi: 10.3934/dcdsb.2010.14.1419 [18] Fuqin Sun, Mingxin Wang. Non-existence of global solutions for nonlinear strongly damped hyperbolic systems. Discrete & Continuous Dynamical Systems, 2005, 12 (5) : 949-958. doi: 10.3934/dcds.2005.12.949 [19] Tatsien Li, Libin Wang. Global exact shock reconstruction for quasilinear hyperbolic systems of conservation laws. Discrete & Continuous Dynamical Systems, 2006, 15 (2) : 597-609. doi: 10.3934/dcds.2006.15.597 [20] Norimichi Hirano, Wieslaw Krawcewicz, Haibo Ruan. Existence of nonstationary periodic solutions for $\Gamma$-symmetric Lotka-Volterra type systems. Discrete & Continuous Dynamical Systems, 2011, 30 (3) : 709-735. doi: 10.3934/dcds.2011.30.709

2019 Impact Factor: 1.338

## Metrics

• PDF downloads (75)
• HTML views (0)
• Cited by (6)

## Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]