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Existence and upper semicontinuity of uniform attractors in $H ¹ (ℝ^{N})$ for nonautonomous nonclassical diffusion equations

Cung The Anh; Nguyen Duong Toan — 2014

Annales Polonici Mathematici

We prove the existence of uniform attractors $_{ε}$ in the space $H ¹ (ℝ^{N})$ for the nonautonomous nonclassical diffusion equation $u_{t} - ε Δ u_{t} - Δ u + f (x, u) + λ u = g (x, t)$ , ε ∈ [0,1]. The upper semicontinuity of the uniform attractors ${_{ε}}_{ε \in [0, 1]}$ at ε = 0 is also studied.

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Existence and upper semicontinuity of uniform attractors in H ¹ ( ℝ N ) for nonautonomous nonclassical diffusion equations

Existence and upper semicontinuity of uniform attractors in $H ¹ (ℝ^{N})$ for nonautonomous nonclassical diffusion equations