Existence and upper semicontinuity of uniform attractors in $H¹\left({ℝ}^N\right)$ for nonautonomous nonclassical diffusion equations

Cung The Anh, and Nguyen Duong Toan. "Existence and upper semicontinuity of uniform attractors in $H¹(ℝ^N)$ for nonautonomous nonclassical diffusion equations." Annales Polonici Mathematici 111.3 (2014): 271-295. <http://eudml.org/doc/280254>.

@article{CungTheAnh2014,
abstract = {We prove the existence of uniform attractors $_\{ε\}$ in the space $H¹(ℝ^N)$ for the nonautonomous nonclassical diffusion equation $u_t - ε Δu_t - Δu + f(x,u) + λu = g(x,t)$, ε ∈ [0,1]. The upper semicontinuity of the uniform attractors $\{_\{ε\}\}_\{ε∈[0,1]\}$ at ε = 0 is also studied.},
author = {Cung The Anh, Nguyen Duong Toan},
journal = {Annales Polonici Mathematici},
keywords = {unbounded domain; tail estimates; asymptotic a priori estimates},
language = {eng},
number = {3},
pages = {271-295},
title = {Existence and upper semicontinuity of uniform attractors in $H¹(ℝ^N)$ for nonautonomous nonclassical diffusion equations},
url = {http://eudml.org/doc/280254},
volume = {111},
year = {2014},
}

TY - JOUR
AU - Cung The Anh
AU - Nguyen Duong Toan
TI - Existence and upper semicontinuity of uniform attractors in $H¹(ℝ^N)$ for nonautonomous nonclassical diffusion equations
JO - Annales Polonici Mathematici
PY - 2014
VL - 111
IS - 3
SP - 271
EP - 295
AB - We prove the existence of uniform attractors $_{ε}$ in the space $H¹(ℝ^N)$ for the nonautonomous nonclassical diffusion equation $u_t - ε Δu_t - Δu + f(x,u) + λu = g(x,t)$, ε ∈ [0,1]. The upper semicontinuity of the uniform attractors ${_{ε}}_{ε∈[0,1]}$ at ε = 0 is also studied.
LA - eng
KW - unbounded domain; tail estimates; asymptotic a priori estimates
UR - http://eudml.org/doc/280254
ER -