THE STABILITY OF THE SOLUTION FOR A HYPERBOLIC PROBLEM ON R^N

다국어 초록 (Multilingual Abstract)

We examine the generalized quasilinear Kirchhoff’s string equation. The purpose of our work is to study the stability of the solution for this equation.

참고문헌 (Reference)

1 G. Kirchhoff, "Vorlesungen Uber Mechanik" Teubner 1883

2 T. Mizumachi, "The asymptotic behavior of solutions to the Kirchhoff equation with a Viscous damping term" 9 : 211-247, 1997

3 M. Tsutsumi, "Some nonlinear evolution equations of second order" 47 : 950-955, 1971

4 Th. Gallay, "Scaling variables and asymptotic expansions in dambed wave equations" 150 : 42-97, 1998

5 R.L. Pego, "Phase transitions in one-dimensional nonlinear viscoelasticity: admissibility and stability" 97 : 353-394, 1987

6 K. Ono, "On global existence, asymptotic stability and blowing - up of solutions for some degenerate nonlinear wave equations of Kirchhoff type with a strong dissipation" 20 : 151-177, 1997

7 M.P. Matos, "On a hyperbolic equation with strong damping" 34 : 303-311, 1991

8 S. Dunford, "Linear operators, I" Wiley-Interscience 1958

9 S.N. Chow, "Invariant manifolds for ows in Banach spaces" 74 : 285-317, 1988

10 R. Temam, "Infinite- dimensional dynamical systems in mechanics and physics" Springer-Verlag 1997

11 K. Ono, "Global existence, decay, and blow-up of solutions for some mildly degenerate nonlinear Kirchhoff strings" 137 : 273-301, 1997

12 K. Ono, "Global existence and decay properties of solutions for some mildly degenerate nonlinear dissipative Kirchhoff strings" 40 : 255-270, 1997

13 N.I. Karahalios, "Global existence and blow-up results for some nonlinear wave equations on RN" 6 : 155-174, 2001

14 P.G. Papadopoulos, "Global existence and blow-up results for an equation of Kirchhoff type on RN" 17 : 91-109, 2001

15 K.J. Brown, "Global bifurcation results for a semilinear elliptic equation on all of RN" 85 : 77-94, 1996

16 D. Henry, "Geometric Theory of Semilinear Parabolic Equations, Lect. Notes in Math" Springer-Verlag 1981

17 M. Nakao, "Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equation" 214 : 325-342, 1993

18 N.I. Karahalios, "Existence of global attractors for semilinear dissipative wave equations on RN" 157 : 183-205, 1999

19 K. Nishihara, "Degenerate quasilinear hyperbolic equation with strong damping" 27 : 125-145, 1984

20 K. Nishihara, "Decay properties of solutions of some quasilinear hyperbolic equations with stong damping" 21 : 17-21, 1993

21 S.N. Chow, "Ck center unstable manifolds" 108A : 303-320, 1988

22 K. Nishihara, "Asymptotic behaviors of solutions of some nonlinear oscillation equations with strong damping" 4 : 285-295, 1994

23 N.I. Karahalios, "Asymptotic behavior of solutions of some nonlinearly damped wave equation on RN" 18 : 73-87, 2001