The Existence of Global Attractor for a Sixth Order Parabolic Equation
نویسندگان
چکیده
This paper is concerned with a sixth-order parabolic equation which arises naturally as a continuum model for the formation of quantum dots and their faceting. Based on the regularity estimates for the semigroups, iteration technique and the classical existence theorem of global attractors, we prove that the sixth order parabolic equation possesses a global attractor in the H (k ≥ 0) space, which attracts any bounded subset of H(Ω) in the H-norm.
منابع مشابه
The existence of global attractor for a Cahn-Hilliard/Allen-Cahn equation
In this paper, we consider a Cahn-Hillard/Allen-Cahn equation. By using the semigroup and the classical existence theorem of global attractors, we give the existence of the global attractor in H^k(0
متن کاملExistence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
متن کاملGlobal Attractor for a Semilinear Parabolic Equation Involving Grushin Operator
The aim of this paper is to prove the existence of a global attractor for a semilinear degenerate parabolic equation involving the Grushin operator.
متن کاملGlobal attractor for a nonlocal hyperbolic problem on ${mathcal{R}}^{N}$
We consider the quasilinear Kirchhoff's problem$$ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,$$with the initial conditions $ u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; f(u)=|u|^{a}u$ and $(phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} )$ is a positive function. The purpose of our work is to ...
متن کاملAttractors for Nonautonomous Parabolic Equations without Uniqueness
Using the theory of uniform global attractors of multivalued semiprocesses, we prove the existence of a uniform global attractor for a nonautonomous semilinear degenerate parabolic equation in which the conditions imposed on the nonlinearity provide the global existence of a weak solution, but not uniqueness. The Kneser property of solutions is also studied, and as a result we obtain the connec...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014