2025/03/10 by Ruy Coimbra Charão, Charão, Ruy Coimbra, Ryo Ikehata +1 · 2 citations
Computer Science · Engineering · Mathematics · #35B45 #35J05 #35L05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Geotechnical and Geomechanical Engineering #Primary 35L52 #Secondary 35B40
paper · pdf · doi:10.48550/arxiv.2503.06854
openalex publication_date 2025/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the system of elastic waves with critical space dependent damping V(x). We study the Cauchy problem for this model in the 2-dimensional Euclidean space \bf R2, and we obtain faster decay rates of the total energy as time goes to infinity. In the 2-D case we do not have any suitable Hardy type inequality, so generally one has no idea to establish optimal energy decay. We develope a special type of multiplier method combined with some estimates brought by the 2-D Newton potential belonging to the usual Laplacian -Δ, not the operator -a2Δ- (b2-a2)∇ \rm div itself. The property of finite speed propagation is important to get results for this system.