半线性抛物方程在L^(2p)空间中全局吸引子的存在性(英文)

EXISTENCE OF GLOBAL ATTRACTORS FOR SEMILINEAR PARABOLIC EQUATION IN L^(2p) SPACE

本文研究了半线性抛物方程所生成的半群{S(t)}t≥0的吸引子的存在性.利用文献[1]中证明吸引子正则性的思想,分别得到半群{S(t)}t≥0在L^(2p)(Ω)空间中具有一个有界吸收集和一个全局吸引子.

In this article,we investigate the existence of attractor for the semigroup {S（t）}_（t≥0）,which is generated by the semilinear parabolic equation.By using the idea for the proof of regularity of the attractor in[1],we obtain a bounded absorbing set and a global attractor for semigroup {S（t）}_（t≥0） in L^（2p）（Ω）,respectively.