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
1Department of Mathematics Hanoi National University of Education 136 Xuan Thuy, Cau Giay Hanoi, Vietnam
2Department of Mathematics Haiphong University 171 Phan Dang Luu, Kien An Haiphong, Vietnam
Annales Polonici Mathematici, Tome 111 (2014) no. 3, pp. 271-295
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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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