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 and 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 and 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 and 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 and 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 and 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 and 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 and Management Optimization, 2019, 15 (4) : 1795-1807. doi: 10.3934/jimo.2018123
[7]

Xiaojun Zheng, Zhongdan Huan, Jun Liu. On the solvability of a semilinear higher-order elliptic problem for the vector field method in image registration. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022068
[8]

Ben-Yu Guo, Yu-Jian Jiao. Mixed generalized Laguerre-Fourier spectral method for exterior problem of Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2009, 11 (2) : 315-345. doi: 10.3934/dcdsb.2009.11.315
[9]

Yacheng Liu, Runzhang Xu. Potential well method for initial boundary value problem of the generalized double dispersion equations. Communications on Pure and Applied Analysis, 2008, 7 (1) : 63-81. doi: 10.3934/cpaa.2008.7.63
[10]

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 and Optimization, 2020, 10 (1) : 75-92. doi: 10.3934/naco.2019034
[11]

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 and Applied Analysis, 2015, 14 (3) : 759-792. doi: 10.3934/cpaa.2015.14.759
[12]

Vladimir V. Chepyzhov, Anna Kostianko, Sergey Zelik. Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1115-1142. doi: 10.3934/dcdsb.2019009
[13]

Senoussi Guesmia, Abdelmouhcene Sengouga. Some singular perturbations results for semilinear hyperbolic problems. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 567-580. doi: 10.3934/dcdss.2012.5.567
[14]

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
[15]

Ignacio Guerra. A semilinear problem with a gradient term in the nonlinearity. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 137-162. doi: 10.3934/dcds.2021110
[16]

Zhiguo Wang, Yiqian Wang, Daxiong Piao. A new method for the boundedness of semilinear Duffing equations at resonance. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 3961-3991. doi: 10.3934/dcds.2016.36.3961
[17]

Yahong Peng, Yaguang Wang. Reflection of highly oscillatory waves with continuous oscillatory spectra for semilinear hyperbolic systems. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1293-1306. doi: 10.3934/dcds.2009.24.1293
[18]

Rudong Zheng, Zhaoyang Yin. The Cauchy problem for a generalized Novikov equation. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 3503-3519. doi: 10.3934/dcds.2017149
[19]

Do Lan. Regularity and stability analysis for semilinear generalized Rayleigh-Stokes equations. Evolution Equations and Control Theory, 2022, 11 (1) : 259-282. doi: 10.3934/eect.2021002
[20]

Jiabao Su, Zhaoli Liu. A bounded resonance problem for semilinear elliptic equations. Discrete and Continuous Dynamical Systems, 2007, 19 (2) : 431-445. doi: 10.3934/dcds.2007.19.431

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (58)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy