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http://dx.doi.org/10.4134/BKMS.2014.51.5.1299

UNIFORM ATTRACTORS FOR NON-AUTONOMOUS NONCLASSICAL DIFFUSION EQUATIONS ON ℝN  

Anh, Cung The (Department of Mathematics Hanoi National University of Education)
Nguyen, Duong Toan (Department of Mathematics Haiphong University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.5, 2014 , pp. 1299-1324 More about this Journal
Abstract
We prove the existence of uniform attractors $\mathcal{A}_{\varepsilon}$ in the space $H^1(\mathbb{R}^N){\cap}L^p(\mathbb{R}^N)$ for the following non-autonomous nonclassical diffusion equations on $\mathbb{R}^N$, $$u_t-{\varepsilon}{\Delta}u_t-{\Delta}u+f(x,u)+{\lambda}u=g(x,t),\;{\varepsilon}{\in}(0,1]$$. The upper semicontinuity of the uniform attractors $\{\mathcal{A}_{\varepsilon}\}_{{\varepsilon}{\in}[0,1]}$ at ${\varepsilon}=0$ is also studied.
Keywords
nonclassical diffusion equation; uniform attractor; unbounded domain; upper semicontinuity; tail estimates method; asymptotic a priori estimate method;
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