Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

ON THE EXISTENCE OF SOLUTIONS OF QUASILINEAR WAVE EQUATIONS WITH VISCOSITY

  • Published : 2000.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

Let be a bonded domain in N with smooth boundary . In this paper, we consider the existence of solutions of the following problem: (1.1)-div{} - + = , , , , , , where q > 1, p$\geq$1, $\delta$>0, , the Laplacian in N and is a positive function like as .

Keywords

References

  1. Sobolev spaces R. A. Adams
  2. Math. Ann. v.259 Gradient estimates for degenerate diffusion equations N. D. Alikakos;R. Rostamian
  3. Inequalities R. Bellman
  4. J. Math. Anal. Appl. v.47 Gradient estimates for solutions of parabolic equations and systems H. Engler
  5. J. Math. Anal. Appl. v.25 On the existence, uniqueness and stability of the equation ρ$x_tt$ = $E(X_{x})X_xx$ + $X_xxt$ J. Greenberg
  6. Quelques methode de Resolution des probleme aux limites Nonlineaire J. L. Lions
  7. Comm. Math. Phys. v.148 Global existence and exponential stability of small solutions to nonlinear viscoelasticity S. Kawashima;Y. Shibata
  8. J. Math. Anal. Appl. v.204 On global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms T. Matsuyama;R. Ikehata
  9. J. Math. Kyoto Univ. v.33 The global existence, uniqueness of small amplitude solutions to the nonlinear acoustic wave equations K. Mizohata;S. Ukai
  10. Math. Z. v.219 Energy decay for quasilinear wave equation with viscosity M. Nakao
  11. J. Math. Anal. Appl. v.204 Existence of an anti-periodic solution for the quasilinear wave equation with viscosity M. Nakao
  12. Adv. Math. Sci. Appl. v.6 On strong solutions of the quasilinear wave equation with viscosity M. Nakao
  13. J. Sound Vib. v.8 Nonlinear vibration of an elastic string K. Narasimha
  14. Applied Math. Sci. v.68 Infinite dimensional dynamical systems in mechanics and physics R. Temam