On Hyperbolic Differential Equation with Periodic Control Initial Condition

Authors

  • Zainab Abdel Ameer Al-Mustansiriya University
  • Sameer Qasim Hasan Al-Mustansiriya University, College of Education, Math Dep. Iraq

DOI:

https://doi.org/10.31185/wjcm.97

Keywords:

Periodic hyperbolic equation, periodic solution., control initial functions

Abstract

The aim of this paper to study the existence solution of some types of hyperbolic differential equation with periodicity of some controls function as nonlocal initial condition for the equation and the technical and used depended on some interest iniquities.

References

B. H, A. Šiber, M. Soljaci ˇ c, T. Schwartz, M. Segev, and D. N. Christodoulides, “Incoherent white light solitons in logarithmically saturable ´ noninstantaneous nonlinear media,” Phys Rev E, vol. 68, no. 3, pp. 36607–36607, 2003.

D. Martino, S. Falanga, M. Godano, C. Lauro, and G, “Logarithmic Schrödinger-like equation as a model for magma transport,” Europhys Lett, vol. 63, no. 3, pp. 472–475, 2003.

W. Królikowski, D. Edmundson, and O. Bang, “Unified model for partially coherent solitons in logarithmically non- linear media,” Phys Rev E, vol. 61, no. 3, pp. 3122–3126, 2000.

A. Ashyralyev and O. Yildirim, “On Multipoint Nonlocal Boundary Value Problems For Hyperbolic Deferential and Difference, equation,” Taiwanese Journal of Mathematics, vol. 14, no. 1, pp. 165–194, 2010.

A. T. Assanova and Z. M. Kadirbayeva, “Periodic Problem For An Impulsive System Of The Loaded Hyperbolic Equations,” Electronic Journal of Differential Equations, vol. 2018, no. 72, pp. 1–8, 2018.

U. Baltayeva and B. I. Islomov, “Boundary Value Problems For The Loaded Third Order Equations of the Hyperbolic and Mixed Types,” Ufa Mathematical Journal, vol. 3, pp. 15–25, 2011.

M. Gugat and F. M. Hante, On The Turnpike Phenomenon For Optimal Boundary Control Problems with Hyperbolic Systems, arXiv:1806.04438v3 [math.AP] 7 Nov 2018.

W. Littman, Boundary Control Theory For Hyperbolic and Parabolic Partial Differential Equations With Constant Coefficients. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 4e série, tome 5, no 3 (1978), p. 567-580.

. J. M. Coron, B. Andréa-Novel, and G. Bastin, “A Strict Lyapunov Function for Boundary, Control of Hyperbolic Systems of Cnservation Laws,” IEEE Transactions on Automatic control, vol. 52, no. 1, 2007.

H. Sano, N. Akagiri, and S, “Backstepping Boundary Control of First-order Coupled Hyperbolic Partial Integro-differential Equations,” Recent Advances in Applie Mathematics, 2009.

Z. W. and Z Jn, Y. Jx, and L. Hl Nonlinear Diffusion Equation World Scientific, 2001.

S. Li and X. Hui, “Periodic Solution of a quasilinear Parabolic Equation with Nonlinear Convection terms,” Advances in Difference Equations, pp. 206–206, 2012.

G. Dg, “Nonlinear functional analysis. shandong science and technology press,” 2001.

O. Ladyzenskaja, V. Solonnikov, and N. Uraltseva Linear and Quasilinear Equations Parabolic Type Translations of Mathematics Monographs, 1968.

R. A. Hameed, B. Wu, and J. Sun, Periodic Solution of a Quasilinear Parabolic Equation with Nonlocal terms and Neumann Boundary conditions, Boundary value problems, 2013: 34

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Published

2022-12-30

Issue

Section

Mathematics

How to Cite

[1]
Z. Abdel Ameer and S. Qasim Hasan, “On Hyperbolic Differential Equation with Periodic Control Initial Condition ”, WJCMS, vol. 1, no. 4, pp. 156–162, Dec. 2022, doi: 10.31185/wjcm.97.