Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains

2014/03/28 by Anton Savostianov, Savostianov, Anton
Engineering · Mathematics · #35B40 #35B45 #35L70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #math.AP #msc:35B40 #msc:35B45 #msc:35L70

paper · pdf · doi:10.48550/arxiv.1403.7476

arxiv created 2014/03/28 · openalex publication_date 2014/03/28 · arxiv updated 2014/03/31 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

The work is devoted to Dirichlet problem for sub-quintic semi-linear wave equation with damping damping term of the form (-Δ)^α∂_t u, α∈(0,(1)/(2)), in bounded smooth domains of \Bbb R³. It appears that to prove well-posedness and develop smooth attractor theory for the problem we need additional regularity of the solutions, which does not follow from the energy estimate. Considering the original problem as perturbation of the linear one the task is reduced to derivation of Strichartz type estimate for the linear wave equation with fractional damping, which is the main feature of the work. Existence of smooth exponential attractor for the natural dynamical system associated with the problem is also established.

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