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Pullback attractors for non-autonomous reaction-diffusion equations on ℝn

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Abstract

We study the long time behavior of solutions of the non-autonomous reaction-diffusion equation defined on the entire space ℝn when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in L 2(ℝn) and H 1(ℝn), respectively. The pullback asymptotic compactness of solutions is proved by using uniform a priori estimates on the tails of solutions outside bounded domains.

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Authors and Affiliations

  1. Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM, 87801, USA

    Bixiang Wang

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  1. Bixiang Wang
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Correspondence to Bixiang Wang.

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Wang, B. Pullback attractors for non-autonomous reaction-diffusion equations on ℝn . Front. Math. China 4, 563–583 (2009). https://doi.org/10.1007/s11464-009-0033-5

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