2009/02/16 by Antonio Segatti, Sergey Zelik
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Attractor #Boundary (topology) #Bounded function #Combinatorics #Dimension (graph theory) #Domain (mathematical analysis) #Exponential function #Fractal #Fractal dimension #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Obstacle problem #Pure mathematics #Reaction–diffusion system #Semigroup #Simplex #Stability and Controllability of Differential Equations #math.AP #msc:35K55 #msc:37L30
paper · pdf · doi:10.1088/0951-7715/22/11/008
arxiv created 2009/02/16 · openalex publication_date 2009/10/13 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A reaction-diffusion problem with an obstacle potential is considered in a bounded domain of \RN. Under the assumption that the obstacle \K is a closed convex and bounded subset of ℝn with smooth boundary or it is a closed n-dimensional simplex, we prove that the long-time behavior of the solution semigroup associated with this problem can be described in terms of an exponential attractor. In particular, the latter means that the fractal dimension of the associated global attractor is also finite.