一类六阶非线性扩散方程的整体吸引子

Global attractor for a class of sixth-order nonlinear diffusion equation

研究一类由具有二阶导数项的Landau-Ginzburg自由能量泛函导出的六阶非线性扩散方程初边值问题的整体动力学行为.基于解的一致估计以及算子半群的渐近紧性证明了当初值u_(0)∈H^(2)_(per)(Ω)时,方程所张成的算子半群在H^(6)_(per)(Ω)存在一个整体吸引子.该研究结果可以使我们更好地了解六阶非线性扩散方程解长时间行为,为研究两相物质之间相互扩散现象提供理论基础.

We study the global dynamics for the initial-boundary value problem of a class of sixth-order nonlinear diffusion equation arising from the Landau-Ginzburg free energy functional with second order derivative terms.On the basis of the uniform estimates of the solution and the asymptotic compactness of the semigroup,we prove the existence of global attractor in the space H^(6)_(per)(Ω)for the semigroup associated with the sixth-order equation provide that initial value u_(0)belongs to H^(2)_(per)(Ω).Our result can help us better understand the properties of the solutions of the sixth-order nonlinear diffusion equations,and can provide the theoretical foundation for studying the diffusion phenomenon of two phases.