کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
842902 | 1470530 | 2009 | 15 صفحه PDF | دانلود رایگان |
In this paper, we study exponential attractors for an equation with arbitrary polynomial growth nonlinearity ff and inhomogeneous term gg. First, we prove by the ℓℓ-trajectory method that the exponential attractor in L2(Ω)L2(Ω) with g∈H−1(Ω)g∈H−1(Ω). Second, by proving the semigroup satisfying discrete squeezing property, we obtain the exponential attractor in H01(Ω) with g∈L2(Ω)g∈L2(Ω). Because the solutions without higher regularity than L2p−2(Ω)L2p−2(Ω) for gg belong only to L2(Ω)L2(Ω) in the equation, the general method by proving the Lipschitz continuity between L2p−2(Ω)L2p−2(Ω) and L2(Ω)L2(Ω) does not work in our case. Therefore, we give a new method (presented in a theorem) to obtain an exponential attractor in a stronger topology space i.e., L2p−2(Ω)L2p−2(Ω) with g∈Gg∈G (stated in a definition) when it is out of reach for the other known techniques.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 71, Issues 3–4, 1–15 August 2009, Pages 751–765