Global attractors for p-Laplacian equation
By Meiling Yang, Chunyou Sun, Chengkui Zhong. 2007
67 citations recorded by the source corpus.
Abstract The existence of a ( L 2 ( Ω ) , W 0 1 , p ( Ω ) ∩ L q ( Ω ) ) -global attractor is proved for the p-Laplacian equation u t − div ( | ∇ u | p − 2 ∇ u ) + f ( u ) = g on a bounded domain Ω ⊂ R n ( n ⩾ 3 ) with Dirichlet boundary condition, where p ⩾ 2 . The nonlinear term f is supposed to satisfy the polynomial growth condition of arbitrary order c 1 | u | q − k ⩽ f ( u ) u ⩽ c 2 | u | q + k and f ′ ( u ) ⩾ − l , where q ⩾ 2 is arbitrary. There is no other restriction on p and q. The asymptotic compactness of the corresponding semigroup is proved by using a new a priori estimate method, called asymptotic a priori estimate.
Subfields: Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2ffdf74c577c8601e89dfb08029268028dbbbd61
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In Control and Systems Engineering
In Mathematical Physics
Citations in the corpus
- Asymptotic regularity for some dissipative equations (2010, background): “, the model and nonlinearity considered in [32]).”
- On a class of degenerate parabolic equations with dynamic boundary conditions (2011, background): “1) with Dirichlet or Neumann type of boundary conditions can be found in [1, 6, 7, 8] (see also [3, 5, 9, 37, 46, 52]).”
- Existence and continuity of bi-spatial random attractors and application to stochastic semilinear Laplacian equations (2015, background): “Even in the deterministic case, the authors in [23,24,35,36, 40] have utilized several continuities (such as norm-continuity, weak-continuity, norm-to-weak continuity, bounded weak-continuity) in the terminate space to prove invariance of an attracting set.”