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EXPONENTIAL BEHAVIOR FOR SOLUTIONS OF NONLINEAR HYPERBOLIC SYSTEM WITH EPSILON PERTURBATION

김대욱
영남수학회 (Youngnam Mathematical Society)|2023.01|East Asian Mathematical Journal|제39권 제1호|pp. 87-92

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참고문헌

키워드

exponential behaviorepsilon perturbationmodified energy func- tionalepsilon perturbation.
주제분류수학

초록

In this paper, we study the nonlinear hyperbolic system with epsilon perturbationstt − div[c(x)∇s] + (ε − 1)st = |s|γ s. Under the conditions of c,γ and other assumptions, we prove the expo-nential behavior rates of the modified energy perturbation.

Abstract

In this paper, we study the nonlinear hyperbolic system with epsilon perturbationstt − div[c(x)∇s] + (ε − 1)st = |s|γ s. Under the conditions of c,γ and other assumptions, we prove the expo-nential behavior rates of the modified energy perturbation.

참고문헌 (11)

  1. 김대욱, "Mathematical Modelling for the Axially Moving Membrane with Internal Time Delay", East Asian Mathematical Journal, 37(1), pp.141~147 (2021), 영남수학회
  2. F. Li, "Global existence and uniqueness and decay estimates for nonlinear viscoelastic wave equation with boundary dissipation", J Nonlinear Analysis : Real World Applications, 12, pp.1759~1773 (2011)
  3. F. Li, "Uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping", Nonlinear Analysis: Real World Applications, 74, pp.3468~3477 (2011)
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  5. J. L. Lions, "Contemporary Developments of Continuum Mechanics and Partial Differential Equations" (1978), North-Holland
  6. M. Aassila, "On Local Solutions of a Mildly Degenerate Hyperbolic Equation", Journal of Mathematical Analysis and Applications, 238, pp.418~428 (1999)
  7. M. Aassila, "Asymptotic behavior of a nonlinear Kirchhoff type equation with spring boundary conditions", Computers and Mathematics with Applications, 62, pp.3004~3014 (2011)
  8. M. Aassila, "Stabilization for the Kirchhoff type equation from an axially moving heterogeneous string modeling with boundary feedback control", Nonlinear Analysis: Theory, Methods and Applications, 75, pp.3598~3617 (2012)
  9. J. L´ımaco, "Vibrations of elastic string with nonhomogeneous material", Journal of Mathematical Analysis and Applications, 344, pp.806~820 (2008)
  10. 김대욱, "STABILIZATION FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH A NONLINEAR SOURCE", East Asian Mathematical Journal, 32(1), pp.117~128 (2016), 영남수학회[DOI]
  11. 김대욱, "ASYMPTIOTIC BEHAVIOR FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH AN INTERNAL TIME-VARYING DELAY TERM", East Asian Mathematical Journal, 32(3), pp.399~412 (2016), 영남수학회[DOI]

관련 논문AI추천

EXPONENTIAL GROWTH OF SOLUTIONS FOR A QUASILINEAR VISCOELASTIC WAVE EQUATION WITH LOGARITHMIC NONLINEARITY강용한, 황근보영남수학회 · East Asian Mathematical Journal2025 · 제41권 제3호Global solutions of the exponential wave equation with small initial data허형진대한수학회 · 대한수학회보2013 · 제50권 제3호EXPONENTIAL STABILITY FOR THE GENERALIZED KIRCHHOFF TYPE EQUATION IN THE PRESENCE OF PAST AND FINITE HISTORY김대욱영남수학회 · East Asian Mathematical Journal2016 · 제32권 제5호General Decay of Solutions for Viscoelastic Equation with Nonlinear Source Terms강수진, 신기연영남수학회 · East Asian Mathematical Journal2018 · 제34권 제5호ENERGY DECAY AND EXPONENTIAL GROWTH OF SOLUTIONS FOR A VISCOELASTIC WAVE EQUATION WITH LOGARITHMIC SOURCE TERM강용한영남수학회 · East Asian Mathematical Journal2025 · 제41권 제3호SOLUTIONS OF QUASILINEAR WAVE EQUATION WITH STRONG AND NONLINEAR VISCOSITY황진수, Hiroki Tanabe, Shin-ichi Nakagiri대한수학회 · 대한수학회지2011 · 제48권 제4호

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