2020/10/06 by Alessandra Piske, Piske, Alessandra, Ruy Coimbra Charão +3
Engineering · Mathematics · #35B40 #35C20 #35L05 #35S05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2010.02485
openalex publication_date 2020/10/06 · openalex created_date 2020/10/15 · openalex updated_date 2026/07/28
We introduce a new model of the logarithmic type of wave-like equation with a nonlocal logarithmic damping mechanism, which is rather weakly effective as compared with frequently studied fractional damping cases. We consider the Cauchy problem for this new model in the whole space, and study the asymptotic profile and optimal decay and/or blowup rates of solutions as time goes to infinity in L2-sense. The operator L considered in this paper was used to dissipate the solutions of the wave equation in the paper studied by Charao-Ikehata in 2020, and in the low frequency parameters the principal part of the equation and the damping term is rather weakly effective than those of well-studied power type operators.