Uniform Decay Rates and Attractors for Evolution PDE′s with Boundary Dissipation
نویسندگان
چکیده
منابع مشابه
Uniform energy decay rates of hyperbolic equations with nonlinear boundary and interior dissipation
We consider the problem of uniform stabilization of nonlinear hyperbolic equations, epitomized by the following three canonical dynamics: (1) the wave equation in the natural state space L2(Ω) × H(Ω), under nonlinear (and non-local) boundary dissipation in the Dirichlet B.C., as well as nonlinear internal damping; (2) a corresponding Kirchhoff equation in the natural state space [H(Ω) ∩H1 0 (Ω)...
متن کاملDecay Estimates for 1-D Parabolic PDEs with Boundary Disturbances
In this work decay estimates are derived for the solutions of 1-D linear parabolic PDEs with disturbances at both boundaries and distributed disturbances. The decay estimates are given in the 2 L and 1 H norms of the solution and discontinuous disturbances are allowed. Although an eigenfunction expansion for the solution is exploited for the proof of the decay estimates, the estimates do not re...
متن کاملUniform Decay Rates of Solutions to a Structural Acoustics Model with Nonlinear Dissipation
In this work, the asymptotic behavior of solutions to a coupled hyperbolic/parabolic{like system is investigated. It is shown that with both components of the equation being subjected to nonlinear damping (boundary damping for the wave component, interior for the beam), a global uniform stability is attained for all (weak) solutions.
متن کاملStrong Uniform Attractors for Non-autonomous Dissipative Pdes with Non Translation-compact External Forces
We give a comprehensive study of strong uniform attractors of non-autonomous dissipative systems for the case where the external forces are not translation compact. We introduce several new classes of external forces which are not translation compact, but nevertheless allow to verify the attraction in a strong topology of the phase space and discuss in a more detailed way the class of so-called...
متن کاملUniform Decay Rates of Solutions to a Nonlinear Wave Equation with Boundary Condition of Memory Type
In this article we study the hyperbolic problem (1) where R is a bounded region in Rn whose boundary is partitioned into disjoint sets ro, rl. We prove that the dissipation given by the memory term is strong enough to assure exponential (or polynomial) decay provided the relaxation function also decays exponentially (or polynomially). In both cases the solution decays with the same rate of the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1995
ISSN: 0022-0396
DOI: 10.1006/jdeq.1995.1119