논문KCI 등재
GLOBAL ATTRACTOR OF THE WEAKLY DAMPED WAVE EQUATION WITH NONLINEAR BOUNDARY CONDITIONS
대한수학회 (The Korean Mathematical Society)|2012.01|대한수학회논문집 (Communications of the KMS)|제27권 제1호|pp. 97-106
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we rst show that the existence of a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.
Abstract
In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we rst show that the existence of a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.
참고문헌 (12)
- R. B. Anibal, "Attractors for parabolic equations with nonlinear boundary conditions, critical exponents, and singular initial data", J. Differential Equations, 181(1), pp.165~196 (2002)
- A. N. Carvalho, "Attractors for parabolic problems with nonlinear boundary conditions", J. Math. Anal. Appl, 207(2), pp.409~461 (1997)
- G. Chen, "Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain", J. Math. Pures Appl, 58(3), pp.249~273 (1979)
- V. Komornik, "A direct method for the boundary stabilization of the wave equation", J. Math. Pures Appl, 69(1), pp.33~54 (1990)
- I. N. Kostin, "Long-time behavior of solutions to a semilinear wave equation with bound- ary damping", Dynam. Control, 11(4), pp.371~388 (2001)
- J. Lagnese, "Decay of solutions of wave equations in a bounded region with boundary dissipation", J. Differential Equations, 50(2), pp.163~182 (1983)
- I. Lasiecka, "Stabilization of wave and plate-like equations with nonlinear dissipation on the boundary", J. Differential Equations, 79(2), pp.340~381 (1989)
- I. Lasiecka, "Uniform Stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions", Appl. Math. Optim, 25(2), pp.189~224 (1992)
- J. E. Munoz Rivera, "Smoothness effect and decay on a class of nonlinear evolution equation", Ann. Fac. Sci. Toulouse Math, 1(2), pp.237~260 (1992)
- D. Tataru, "Uniform decay rates and attractors for evolution PDE's with boundary dis- sipation", J. Differential Equations, 121(1), pp.1~27 (1995)
- R. Temam, "In nite Dimensional Dynamical Systems in Mechanics and Physics" (1988), Springer
- E. Zuazua, "Stability and decay for a class of nonlinear hyperbolic problems", Asymptotic Anal, 1(2), pp.161~185 (1988)
관련 논문AI추천
GLOBAL ATTRACTOR FOR SOME BEAM EQUATION WITH NONLINEAR SOURCE AND DAMPING TERMS이미진영남수학회 · East Asian Mathematical Journal2016 · 제32권 제3호On solvability of the dissipative Kirchhoff equation with nonlinear boundary dampingJian-Hua Huang, Zai-Yun Zhang대한수학회 · 대한수학회보2014 · 제51권 제1호General decay for a semilinear wave equation with boundary frictional and memory conditions박선혜대한수학회 · 대한수학회보2014 · 제51권 제3호UNIFORM ATTRACTORS FOR NON-AUTONOMOUS NONCLASSICAL DIFFUSION EQUATIONS ON RNCung The Anh, Nguyen Duong Toan대한수학회 · 대한수학회보2014 · 제51권 제5호Global attractors for nonlocal parabolic equations with a new class of nonlinearitiesCung The Anh, Le Tran Tinh, Vu Manh Toi대한수학회 · 대한수학회지2018 · 제55권 제3호Global existence and nonexistence of solutions for coupled nonlinear wave equations with damping and source termsYaojun Ye대한수학회 · 대한수학회보2014 · 제51권 제6호