2021/04/17 by Ruy Coimbra Charão, Charao, Ruy Coimbra, Alessandra Piske +3
Computer Science · Engineering · Mathematics · #35B40 #35C20 #35L05 #35S05 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2104.08468
openalex publication_date 2021/04/17 · openalex created_date 2022/11/27 · openalex updated_date 2026/07/28
We introduce a new model of the logarithmic type of wave like plate equation with a nonlocal logarithmic damping mechanism. We consider the Cauchy problem for this new model in the whole space, and study the asymptotic profile and optimal decay rates of solutions as time goes to infinity in L2-sense. The operator L considered in this paper was first introduced to dissipate the solutions of the wave equation in the paper studied by Charao-Ikehata in 2020. We will discuss the asymptotic property of the solution as time goes to infinity to our Cauchy problem, and in particular, we classify the property of the solutions into three parts from the viewpoint of regularity of the initial data, that is, diffusion-like, wave-like, and both of them.