Geodesic
Existence and upper semicontinuity of uniform attractors in $H^1(\mathbb {R}^N)$ for nonautonomous nonclassical diffusion equations
Cung The Anh1 ; Nguyen Duong Toan2
1 Department of Mathematics Hanoi National University of Education 136 Xuan Thuy, Cau Giay Hanoi, Vietnam
2 Department of Mathematics Haiphong University 171 Phan Dang Luu, Kien An Haiphong, Vietnam
Annales Polonici Mathematici, Tome 111 (2014) no. 3, pp. 271-295 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove the existence of uniform attractors $\mathcal A_{\varepsilon }$ in the space $H^1(\mathbb {R}^N)$ for the nonautonomous nonclassical diffusion equation $$ u_t - \varepsilon \varDelta u_t - \varDelta u + f(x,u)+\lambda u = g(x,t),\hskip 1em \varepsilon \in [0,1]. $$ The upper semicontinuity of the uniform attractors $\{\mathcal A_{\varepsilon }\}_{\varepsilon \in [0,1]}$ at $\varepsilon = 0$ is also studied.
DOI : 10.4064/ap111-3-5
Keywords: prove existence uniform attractors mathcal varepsilon space mathbb nonautonomous nonclassical diffusion equation varepsilon vardelta vardelta lambda hskip varepsilon upper semicontinuity uniform attractors mathcal varepsilon varepsilon varepsilon studied

Cung The Anh 1 ; Nguyen Duong Toan 2

1 Department of Mathematics Hanoi National University of Education 136 Xuan Thuy, Cau Giay Hanoi, Vietnam
2 Department of Mathematics Haiphong University 171 Phan Dang Luu, Kien An Haiphong, Vietnam 
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Cung The Anh; Nguyen Duong Toan. Existence and upper semicontinuity of uniform attractors in $H^1(\mathbb {R}^N)$ for nonautonomous nonclassical diffusion equations. Annales Polonici Mathematici, Tome 111 (2014) no. 3, pp. 271-295. doi: 10.4064/ap111-3-5

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