منابع مشابه
Global Attractors for Damped Semilinear Wave Equations
The existence of a global attractor in the natural energy space is proved for the semilinear wave equation utt + βut − ∆u + f(u) = 0 on a bounded domain Ω ⊂ R with Dirichlet boundary conditions. The nonlinear term f is supposed to satisfy an exponential growth condition for n = 2, and for n ≥ 3 the growth condition |f(u)| ≤ c0(|u|γ + 1), where 1 ≤ γ ≤ n n−2 . No Lipschitz condition on f is assu...
متن کاملInertial manifolds of damped semilinear wave equations
© AFCET, 1989, tous droits réservés. L’accès aux archives de la revue « Modélisation mathématique et analyse numérique » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de cop...
متن کاملRegularity of the global attractor for semilinear damped wave equations
utt + 2ηA 1 2 ut + aut + Au = f(u) in H1 0 (Ω)×L2(Ω), where Ω is a bounded smooth domain in R3. For dissipative nonlinearity f ∈ C2(R,R) satisfying |f ′′(s)| ≤ c(1 + |s|) with some c > 0, we prove that the family of attractors {Aη , η ≥ 0} is upper semicontinuous at η = 0 in H1+s(Ω)×Hs(Ω) for any s ∈ (0, 1). For dissipative f ∈ C3(R,R) satisfying lim|s|→∞ f ′′(s) s = 0 we prove that the attract...
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 کاملAsymptotic behaviour of strongly damped nonlinear hyperbolic equations
© AFCET, 1989, tous droits réservés. L’accès aux archives de la revue « Modélisation mathématique et analyse numérique » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de cop...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics and Stochastic Analysis
سال: 1995
ISSN: 1048-9533,1687-2177
DOI: 10.1155/s1048953395000360