an:06986346
Zbl 1410.35101
Su, Keqin; Qin, Yuming
The pullback-\(\mathcal{D}\) attractors for the 3D Kelvin-Voigt-Brinkman-Forchheimer system with delay
EN
Math. Methods Appl. Sci. 41, No. 16, 6122-6129 (2018).
00421041
2018
j
35Q30 37L30 35B40 35B41 35G31
continuous delay; Kelvin-Voigt-Brinkman-Forchheimer system; pullback-$\mathcal{D}$ attractors
The authors consider the 3D Kelvin-Voigt-Brinkman-Forchheimer system with continuous delay and prove the existence of pullback-$\mathcal{D}$ attractors. The method of proof involves establishing the existence of pullback-$\mathcal{D}$ absorbing sets and the pullback-$\mathcal{D}$ asymptotic compactness of the associated family of solution processes. The asymptotic compactness result follows the standard decomposition technique for hyperbolic/wave equations treated for non-autonomous source terms (cf. e.g. [\textit{V. V. Chepyzhov} and \textit{M. I. Vishik}, Attractors for equations of mathematical physics. Providence, RI: American Mathematical Society (AMS) (2002; Zbl 0986.35001)]).
Joseph Shomberg (Providence)
Zbl 0986.35001