2018/02/04 by Maíra Fernandes Gauer Palma, Palma, M. F. G., Cleverson Roberto da Luz +2 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1802.01112
openalex publication_date 2018/02/04 · openalex created_date 2022/08/16 · openalex updated_date 2026/07/28
In this work we study the asymptotic behavior of solutions for a general\nlinear second-order evolution differential equation in time with fractional\nLaplace operators in \ℝn. We obtain improved decay estimates with\nless demand on the initial data when compared to previous results in the\nliterature. In certain cases, we observe that the dissipative structure of the\nequation is of regularity-loss type. Due to that special structure, to get\ndecay estimates in high frequency region in the Fourier space it is necessary\nto impose additional regularity on the initial data to obtain the same decay\nestimates as in low frequency region. The results obtained in this work can be\napplied to several initial value problems associated to second-order equations,\nas for example, wave equation, plate equation, IBq, among others.\n