American Institute of Mathematical Sciences

Advanced
  • Previous Article
    A priori estimates of global solutions of superlinear parabolic problems without variational structure
  • DCDS Home
  • This Issue
  • Next Article
    Convergence to strong nonlinear rarefaction waves for global smooth solutions of $p-$system with relaxation
September  2003, 9(5): 1263-1275. doi: 10.3934/dcds.2003.9.1263

Generalized quasilinearization method for semilinear hyperbolic problems

T. Gnana Bhaskar 1, , S. Köksal 1, and  V. Lakshmikantham 2,

1. 

Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, United States, United States
2. 

Department of Mathematics, Florida Institute of Technology, Melbourne, FL 32901, United States

Received  November 2001 Revised  November 2002 Published  June 2003

We consider semilinear hyperbolic problem associated with a second order partial differential operator in its divergence form. We prove a comparison theorem for the weak lower and upper solutions of the problem and then apply the method of generalized quasilinearization.
Keywords: Semilinear hyperbolic problem, generalized quasilinearization method..
Mathematics Subject Classification: 34D10, 34D9.
Citation: T. Gnana Bhaskar, S. Köksal, V. Lakshmikantham. Generalized quasilinearization method for semilinear hyperbolic problems. Discrete & Continuous Dynamical Systems, 2003, 9 (5) : 1263-1275. doi: 10.3934/dcds.2003.9.1263
[1]

V. Lakshmikantham, S. Leela. Generalized quasilinearization and semilinear degenerate elliptic problems. Discrete & Continuous Dynamical Systems, 2001, 7 (4) : 801-808. doi: 10.3934/dcds.2001.7.801
[2]

Akisato Kubo. Asymptotic behavior of solutions of the mixed problem for semilinear hyperbolic equations. Communications on Pure & Applied Analysis, 2004, 3 (1) : 59-74. doi: 10.3934/cpaa.2004.3.59
[3]

Kaifang Liu, Lunji Song, Shan Zhao. A new over-penalized weak galerkin method. Part Ⅰ: Second-order elliptic problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2411-2428. doi: 10.3934/dcdsb.2020184
[4]

Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2581-2598. doi: 10.3934/dcdsb.2020196
[5]

Fengming Ma, Yiju Wang, Hongge Zhao. A potential reduction method for the generalized linear complementarity problem over a polyhedral cone. Journal of Industrial & Management Optimization, 2010, 6 (1) : 259-267. doi: 10.3934/jimo.2010.6.259
[6]

Xiaona Fan, Li Jiang, Mengsi Li. Homotopy method for solving generalized Nash equilibrium problem with equality and inequality constraints. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1795-1807. doi: 10.3934/jimo.2018123
[7]

Ben-Yu Guo, Yu-Jian Jiao. Mixed generalized Laguerre-Fourier spectral method for exterior problem of Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2009, 11 (2) : 315-345. doi: 10.3934/dcdsb.2009.11.315
[8]

Yacheng Liu, Runzhang Xu. Potential well method for initial boundary value problem of the generalized double dispersion equations. Communications on Pure & Applied Analysis, 2008, 7 (1) : 63-81. doi: 10.3934/cpaa.2008.7.63
[9]

Ouayl Chadli, Gayatri Pany, Ram N. Mohapatra. Existence and iterative approximation method for solving mixed equilibrium problem under generalized monotonicity in Banach spaces. Numerical Algebra, Control & Optimization, 2020, 10 (1) : 75-92. doi: 10.3934/naco.2019034
[10]

Zhi-Qiang Shao. Lifespan of classical discontinuous solutions to the generalized nonlinear initial-boundary Riemann problem for hyperbolic conservation laws with small BV data: shocks and contact discontinuities. Communications on Pure & Applied Analysis, 2015, 14 (3) : 759-792. doi: 10.3934/cpaa.2015.14.759
[11]

Vladimir V. Chepyzhov, Anna Kostianko, Sergey Zelik. Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1115-1142. doi: 10.3934/dcdsb.2019009
[12]

Senoussi Guesmia, Abdelmouhcene Sengouga. Some singular perturbations results for semilinear hyperbolic problems. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 567-580. doi: 10.3934/dcdss.2012.5.567
[13]

Junping Shi, R. Shivaji. Semilinear elliptic equations with generalized cubic nonlinearities. Conference Publications, 2005, 2005 (Special) : 798-805. doi: 10.3934/proc.2005.2005.798
[14]

Ignacio Guerra. A semilinear problem with a gradient term in the nonlinearity. Discrete & Continuous Dynamical Systems, 2022, 42 (1) : 137-162. doi: 10.3934/dcds.2021110
[15]

Zhiguo Wang, Yiqian Wang, Daxiong Piao. A new method for the boundedness of semilinear Duffing equations at resonance. Discrete & Continuous Dynamical Systems, 2016, 36 (7) : 3961-3991. doi: 10.3934/dcds.2016.36.3961
[16]

Yahong Peng, Yaguang Wang. Reflection of highly oscillatory waves with continuous oscillatory spectra for semilinear hyperbolic systems. Discrete & Continuous Dynamical Systems, 2009, 24 (4) : 1293-1306. doi: 10.3934/dcds.2009.24.1293
[17]

Rudong Zheng, Zhaoyang Yin. The Cauchy problem for a generalized Novikov equation. Discrete & Continuous Dynamical Systems, 2017, 37 (6) : 3503-3519. doi: 10.3934/dcds.2017149
[18]

Do Lan. Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021002
[19]

Jian Hou, Liwei Zhang. A barrier function method for generalized Nash equilibrium problems. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1091-1108. doi: 10.3934/jimo.2014.10.1091
[20]

Hao-Chun Lu. An efficient convexification method for solving generalized geometric problems. Journal of Industrial & Management Optimization, 2012, 8 (2) : 429-455. doi: 10.3934/jimo.2012.8.429

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (48)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy