Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 4
129
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Existence and asymptotic stability of solutions for a hyperbolic equation with logarithmic source

Pages 1144-1160 | Received 07 Feb 2021, Accepted 06 Sep 2021, Published online: 16 Sep 2021

References

  • Bialynicki-Birula I, Mycielski J. Wave equations with logarithmic nonlinearities. Bull Acad Polon Sci Ser Sci Math Astronom Phys. 1975;23(4):461–466.
  • Bialynicki-Birula I, Mycielski J. Nonlinear wave mechanics. Ann Phys. 1976;100(1-2):62–93.
  • Bartkowski K, Gorka P. One-dimensional Klein-Gordon equation with logarithmic nonlinearities. J Phys A. 2008;41(35):355201.
  • Gorka P. Logarithmic Klein-Gordon equation. Acta Phys Polon B. 2009;40(1):59–66.
  • Koutvitsky VA, Maslov EM. Instability of coherent states of a real scalar field. J Math Phys. 2006;47(2):022302.
  • Cavalcanti MM, Domingos Cavalcanti VN, Lasiecka I. Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction. J Differ Equ. 2007;236:407–459.
  • Cavalcanti MM, Domingos Cavalcanti VN, Martinez P. Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term. J Differ Equ. 2004;203:119–158.
  • Ha TG. Asymptotic stability of the viscoelastic equation with variable coefficients and the Balakrishnan-Taylor damping. Taiwanese J Math. 2018;22(4):931–948.
  • Ha TG. Energy decay for the wave equation of variable coefficients with acoustic boundary conditions in domains with nonlocally reacting boundary. Appl Math Lett. 2018;76:201–207.
  • Ha TG. Energy decay rate for the wave equation with variable coefficients and boundary source term. Appl Anal. 2021;100(11):2301–2314.
  • Ha TG. Global existence and general decay estimates for the viscoelastic equation with acoustic boundary conditions. Discrete Contin Dyn Syst. 2016;36:6899–6919.
  • Komornik V, Zuazua E. A direct method for boundary stabilization of the wave equation. J Math Pures Appl. 1990;69:33–54.
  • Lasiecka I, Tataru D. Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping. Differ Integral Equ. 1993;6(3):507–533.
  • Chen H, Tian S. Initial boundary value problem for a class of semilinear pseudo-parabloic equations with logarithmic nonlinearity. J Differ Equ. 2015;258:4424–4442.
  • Ha TG, Park SH. Blow-up phenomena for a viscoelastic wave equation with strong damping and logarithmic nonlinearity. Adv Differ Equ. 2020;2020:235.
  • He Y, Gao H, Wang H. Blow-up and decay for a class of pseudo-parabolic p-Laplacian equation with logarithmic nonlinearity. Comput Math Appl. 2018;75:459–469.
  • Ji S, Yin J, Cao Y. Instability of positive periodic solutions for semilinear pseudo-parabolic equations with logarithmic nonlinearity. J Differ Equ. 2016;261:5446–5464.
  • Chen H, Luo P, Liu G. Global solution and blow-up of a semilinear heat equation with logarithmic nonlinearity. J Math Anal Appl. 2015;422:84–98.
  • Nhan LC, Truong LX. Global solution and blow-up for a class of pseudo-p-Laplacian evolution equations with logarithmic nonlinearity. Comput Math Appl. 2017;73:2076–2091.
  • Ma L, Fang ZB. Energy decay estimates and infinite blow-up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source. Math Meth Appl Sci. 2018;41:2639–2653.
  • Ha TG. Sufficient condition for logarithmic nonlinearity in nonlinear evolution equations. Math Meth Appl Sci. 2021;44:9611–9615.
  • Martinez P. A new method to obtain decay rate estimates for dissipative systems with localized damping. Rev Mat Compl. 1999;12:251–283.
  • Gross L. Logarithmic sobolev inequalities. Am J Math. 1975;97(4):1061–1083.
  • Cazenave T, Haraux A. Équations d'évolution avec non-linéarité logarithmique. Ann Fac Sci Toulouse Math. 1980;2(1):21–51.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.