2010/06/14 by Mickaël D. Chekroun, Chekroun, Mickaël D., Francesco Di Plinio +5
Mathematics · Physics and Astronomy · #35K05 #47H20 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 35B41 #Secondary: 45K05 #math-ph #math.AP #math.DS #math.MP #msc:35B41 #msc:35K05 #msc:45K05 #msc:47H20
paper · pdf · doi:10.48550/arxiv.1006.2579
Accepted in Discrete and Continuous Dynamical Systems, Serie S
arxiv created 2010/06/14 · arxiv updated 2010/06/15
This paper is concerned with the integrodifferential equation ∂t u-Δu -∫0^∞ κ(s)Δu(t-s) \d s + φ(u)=f arising in the Coleman-Gurtin's theory of heat conduction with hereditary memory, in presence of a nonlinearity φ of critical growth. Rephrasing the equation within the history space framework, we prove the existence of global and exponential attractors of optimal regularity and finite fractal dimension for the related solution semigroup, acting both on the basic weak-energy space and on a more regular phase space.