R^n上具有记忆项的非自治反应扩散方程的拉回吸引子的存在性

The existence of pullback attractor for non-autonomous reaction-diffusion equations with memory term on R^n

研究了如下在无界区域Rn上具有线性记忆项和在相空间中无界的外力项的非自治反应扩散方程的解的长时间行为u/t-Δu+λu-∫∞0k(s)Δu(t-s)ds=f(x,u)+g(x,t).运用一致先验估计方法证明了解的拉回渐近紧性,进而证明了方程分别在相空间X0=L2(Rn)×M0和X1=H1(Rn)×M1上的拉回吸引子的存在性.

We study the long time behavior of the following non-autonomous reaction-diffusion equation defined on the unbounded domain Rn with a linear memory term and external terms which are unbounded in a phase space u/t-Δu＋λu-∫∞0k（s）Δu（t-s）ds=f（x,u）＋g（x,t）. We use the uniform estimates method to prove the existence of the pullback attractor for the above equation in phase space X0=L2（Rn）×M0 and X1=H1（Rn）×M1,respectively.