Rodríguez Bernal, Aníbal and Vidal López, Alejandro and Robinson, James C. (2007) Pullback attractors and extremal complete trajectories for nonautonomous reactiondiffusion problems. Journal of Differential Equations, 238 (2). 289337 . ISSN 00220396

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Official URL: http://www.sciencedirect.com/science/journal/00220396
Abstract
We analyse the dynamics of the nonautonomous nonlinear reaction–diffusion equation ut −_u = f (t,x,u),
subject to appropriate boundary conditions, proving the existence of two bounding complete trajectories, one maximal and one minimal. Our main assumption is that the nonlinear term satisfies a bound of the form f (t,x,u)u _ C(t, x)u2 + D(t, x)u, where the linear evolution operator associated with _ + C(t, x) is exponentially stable. As an important step in our argument we give a detailed analysis of the exponential stability properties of the evolution operator for the nonautonomous linear problem ut − _u = C(t, x)u
between different Lp spaces.
Item Type:  Article 

Uncontrolled Keywords:  Pullback attractors; Extremal complete trajectories; Reactiondiffusion equation; Evolution operator; Exponentially stable; Nonautonomous logistic equation 
Subjects:  Sciences > Mathematics > Differential equations 
ID Code:  12776 
Deposited On:  27 May 2011 08:31 
Last Modified:  06 Feb 2014 09:32 
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