DYNAMICS OF NON - AUTONOMOUS NONCLASSICAL DIFFUSION EQUATIONS ON R n Cung
نویسنده
چکیده
We consider the Cauchy problem for a non-autonomous nonclassical diffusion equation of the form ut − ε∆ut −∆u+ f(u) + λu = g(t) on Rn. Under an arbitrary polynomial growth order of the nonlinearity f and a suitable exponent growth of the external force g, using the method of tail-estimates and the asymptotic a priori estimate method, we prove the existence of an (H1(Rn) ∩ Lp(Rn), H1(Rn) ∩ Lp(Rn)) pullback attractor Âε for the process associated to the problem. We also prove the upper semicontinuity of {Âε : ε ∈ [0, 1]} at ε = 0.
منابع مشابه
Uniform Attractors for Non-autonomous Nonclassical Diffusion Equations on R
where ε ∈ [0, 1], the nonlinearity f and the external force g satisfy some certain conditions specified later. This equation is known as the nonclassical diffusion equation when ε > 0, and the reaction-diffusion equation when ε = 0. Nonclassical diffusion equation arises as a model to describe physical phenomena, such as non-Newtonian flows, soil mechanic, and heat conduction (see, e.g., [1, 7,...
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