Pullback attractors and extremal complete trajectories for non-autonomous reaction–diffusion problems
Pullback attractors and extremal complete trajectories for non-autonomous reaction–diffusion problems
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DOI：
10.1016/j.jde.2007.03.028
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发表时间：
2007-07
影响因子：
2.4
通讯作者：
James C. Robinson;A. Rodríguez-Bernal;Alejandro Vidal-L'opez
中科院分区：
文献类型：
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作者：
James C. Robinson;A. Rodríguez-Bernal;Alejandro Vidal-L'opez
我们分析了在适当边界条件下的非自主非线性反应扩散方程的动力学，证明了两种边界完整轨迹的存在，一种是最大的，一种是最小的。我们的主要假设是非线性项满足 f(t,x,u)u⩽C(t,x)|u|2+D(t,x)|u| 形式的界限，其中与 Δ+C(t,x) 相关的线性演化算子是指数稳定的。作为我们论证的重要一步，我们详细分析了不同 Lp 空间之间的非自治线性问题 ut−Δu=C(t,x)u 的演化算子的指数稳定性特性。
We analyse the dynamics of the non-autonomous nonlinear reaction–diffusion equation 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 Δ+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−Δu=C(t,x)u between different Lpspaces.