Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 2
77
Views
2
CrossRef citations to date
0
Altmetric
Research Article

On the fractional order hyperbolic equation with random coefficients

Pages 590-609 | Received 23 Apr 2021, Accepted 06 Jul 2021, Published online: 31 Jul 2021

References

  • He D, Witt I, Yin H. On semilinear Tricomi equations with critical exponents or in two space dimensions. J Differ Equ. 2017;263:8102–8137.
  • Mezadek AK, Reissig M. Semi-linear fractional σ-evolution equations with mass or power non-linearity. Nonlinear Differ Equ App. 2018;42:1–43.
  • do Nascimento WN, Palmieri A, Reissig M. Semi-linear wave models with power non-linearity and scale-invariant time-dependent mass and dissipation. Math Nathr. 2017;290:1779–1805.
  • Palmieri A, Reissig M. Semi-linear wave models with power non-linearity and scale-invariant time-dependent mass and dissipation, II. Math Nathr. 2017;291:1859–1892.
  • Colombini F, Lerner N. Hyperbolic operators with non-Lipschitz coefficients. Duke Math J. 1995;77:657–698.
  • Colombini F, Del Santo D, Reissig M. On the optimal regularity of coefficients in hyperbolic Cauchy problems. Bull Sc Math 127. 2003;4:328–347.
  • Cicognani M, Hirosawa F, Reissig M. The log-effect for p-evolution type models. J Math Soc Japan 2008; doi:10.2969/jmsj/06030819.
  • Hirosawa F. On the Cauchy problem for second order strictly hyperbolic equations with non-regular coefficients. Math Nach. 2003;256:29–47.
  • Hirosawa F. Loss of regularity for the solutions to hyperbolic equations with non-regular coefficients, an application to Kirchhoff equation. MMAS. 2003;26(9):783–799.
  • Wu Y, Lu X. Regularity of hyperbolic magnetic Schrödinger equation with oscillating coefficients. J Differ Equ. 2017;263:1966–1985.
  • Guo B, Pu X, Huang F. Fractional partial differential equations and their numerical solutions. Beijing: Science Press; 2012.
  • Øksendal B. Stochastic differential equations: an introduction with applications. 6th ed. Berlin: Springer Verlag; 2005.
  • Taylor Michael E. Pseudodifferential operators. Princeton, NJ: Princeton Univ. Press; 1981.
  • Xu Q. Stochastic processes with its applications. Beijing: Higher Education Press; 2015.
  • Lu X. On the magnetic Schrödinger hyperbolic equation with randomized coefficients. Z Angew Math Mech. 2021;e202000127:1–26. doi:10.1002/zamm.202000127.
  • Hirosawa F, Reissig M. Levi condition for hyperbolic equations with oscillating coefficients. J Differ Equ. 2006;223:329–350.
  • Lu X. On the optimal regularity of plate equations with randomized time-dependent coefficients. Z Angew Math Mech. 2018;98(7):1224–1236.
  • Lu X, Reissig M. Instability behavior and loss of regularity. Advances in phase space analysis of partial differential equations. Boston: Birkhäuser Verlag; 2009. p. 171–200.
  • Lu X, Reissig M. Does the loss of regularity really appear? Math Methods Appl Sci. 2009;32:1183–1324.
  • Bourgain J. A remark on normal forms and the I-method for periodic NLS. J Anal Math. 2004;94:125–157.
  • Alabau-Boussouira F. Convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems. Appl Math Optim. 2005;51:61–105.
  • Fang D, Lu X, Reissig M. ν-loss of derivatives for an evolution type model. Nonlinear Anal. 2009;71:5368–5380.

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.