On Global Attractors for a Nonlinear Parabolic Equation of m-Laplacian Type in RN

Abstract

Abstract. We prove the existence, some absorbing properties and some regularities of ðL 2 ðR N Þ; L p ðR N ÞÞ, 2 a p < y, global attractor for the m-Laplacian type quasilinear parabolic equation in R N with a perturbation gðx; uÞ þ f ðxÞ.

Global Attractor for Some Beam Equation With Nonlinear Source and Damping Terms

“…Here we use the facts Then by definition E w (t) and (17) By applying Lemma 2.1 we can derive (13). So we prove that S(t) is asymptotically smooth.…”

“…In [17], the authors showed the existence of global attractor for plate equation with nonlinear damping. In [13,14], the authors dealt with the global attractor for nonlinear parabolic equation of mLaplace type in R N . Recently, the research of beam equations have attracted considerable attention(see [1,2,4,5] and reference there in).…”

Well-posedness and attractor for a strongly damped wave equation with supercritical nonlinearity on $ \mathbb{R}^{N} $

“…Another approach is working in usual Sobolev spaces (cf. [12,21,23,24,25]). By combining the decomposition of the solution and the tail cut-off technique, Belleri and Pata [4] obtained the existence of global attractor for the strongly damped wave equation on R 3 :…”