On the dynamics of a class of nonclassical parabolic equations

By Suyun Wang, Desheng Li, Chengkui Zhong. 2006

95 citations recorded by the source corpus.

Abstract We consider the first initial and boundary value problem of nonclassical parabolic equations u t − μ Δ u t − Δ u + g ( u ) = f ( x ) on a bounded domain Ω , where μ ∈ [ 0 , 1 ] . First, we establish some uniform decay estimates for the solutions of the problem which are independent of the parameter μ . Then we prove the continuity of solutions as μ → 0 . Finally we show that the problem has a unique global attractor A μ in V 2 = H 2 ( Ω ) ∩ H 0 1 ( Ω ) in the topology of H 2 ( Ω ) ; moreover, A μ → A 0 in the sense of Hausdorff semidistance in H 0 1 ( Ω ) as μ goes to 0.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/385a6e9a72672256edfe915557f2a213984a33a6