Attractors for nonclassical diffusion equations with arbitrary polynomial growth nonlinearity

作者：Xie, Yongqin^*; Li, Qingsong; Zhu, Kaixuan

来源：Nonlinear Analysis: Real World Applications , 2016, 31: 23-37.

DOI：10.1016/j.nonrwa.2016.01.004

• Asymptotic contractive semigroup
• Nonclassical diffusion equation
• Global attractor
• The whole space
• Polynomial growth of arbitrary order

In this paper, using a new method (or technique) called "Asymptotic Contractive Semigroup Method" (see Theorem 2.3) we prove the existence of global attractor for the nonclassical diffusion equations in H-1(R-n). The nonlinearity satisfies the arbitrary order polynomial growth conditions and the forcing term g only belongs to H-1(R-n). The results obtained essentially improve and complement in some previously published papers.

• 出版日期2016-10
• 单位长沙理工大学; 兰州大学