On decay properties of solutions for degenerate strongly damped wave equations of Kirchhoff type
نویسندگان
چکیده
منابع مشابه
Decay of solutions of some degenerate hyperbolic equations of Kirchhoff type
In this paper we study the asymptotic behavior of solutions to the damped, nonlinear vibration equation with self-interaction ü = −γu̇+m(‖∇u‖)∆u− δ|u|u+ f, which is known as degenerate if m(·) ≥ 0, and non-degenerate if m(·) ≥ m0 > 0. We would like to point out that, to the author’s knowledge, exponential decay for this type of equations has been studied just for the special cases of α. Our aim ...
متن کاملEnergy decay for damped wave equations on partially rectangular domains
We consider the wave equation with a damping term on a partially rectangular planar domain, assuming that the damping is concentrated close to the non-rectangular part of the domain. Polynomial decay estimates for the energy of the solution are established.
متن کاملSpectral gap global solutions for degenerate Kirchhoff equations
We consider the second order Cauchy problem u +m(|Au|)Au = 0, u(0) = u0, u(0) = u1, where m : [0,+∞) → [0,+∞) is a continuous function, and A is a self-adjoint nonnegative operator with dense domain on a Hilbert space. It is well known that this problem admits local-in-time solutions provided that u0 and u1 are regular enough, depending on the continuity modulus of m, and on the strict/weak hyp...
متن کاملOn the Existence of Solutions of Strongly Damped Nonlinear Wave Equations
We investigate the existence and uniqueness of solutions of the following equation of hyperbolic type with a strong dissipation: utt(t,x)− ( α+β (∫ Ω |∇u(t,y)|2dy )γ) ∆u(t,x) −λ∆ut(t,x)+μ|u(t,x)|q−1u(t,x)= 0, x ∈Ω, t ≥ 0, u(0,x)=u0(x), ut(0,x)=u1(x), x ∈Ω, u|∂Ω = 0, where q > 1, λ > 0, μ ∈R, α, β≥ 0, α+β > 0, and ∆ is the Laplacian in RN .
متن کاملAttractors for Strongly Damped Wave Equations with Critical Nonlinearities
In this paper we obtain global well-posedness results for the strongly damped wave equation utt + (−∆)θut = ∆u + f(u), for θ ∈ [1 2 , 1 ] , in H 0(Ω)×L(Ω) when Ω is a bounded smooth domain and the map f grows like |u|n+2 n−2 . If f = 0, then this equation generates an analytic semigroup with generator −A(θ). Special attention is devoted to the case when θ = 1 since in this case the generator −A...
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 Mathematical Analysis and Applications
سال: 2011
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.03.034