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Rodríguez Bernal, Aníbal and Vidal López, Alejandro and Robinson, James C.
(2007)
*Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems.*
Journal of Differential Equations, 238
(2).
289-337 .
ISSN 0022-0396

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Official URL: http://www.sciencedirect.com/science/journal/00220396

## Abstract

We analyse the dynamics of the non-autonomous 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)|u|2 + 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 non-autonomous linear problem ut − _u = C(t, x)u

between different Lp spaces.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Pullback attractors; Extremal complete trajectories; Reaction-diffusion equation; Evolution operator; Exponentially stable; Non-autonomous logistic equation |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 12776 |

Deposited On: | 27 May 2011 08:31 |

Last Modified: | 12 Dec 2018 15:07 |

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