σ-Evolution models with low regular time-dependent non-effective structural damping

Article type: Research Article

Authors: Vargas Junior, Edson Cilos^{; *} | da Luz, Cleverson Roberto

Affiliations: Department of Mathematics, Federal University of Santa Catarina, Brazil. E-mails: [email protected], [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this work we study decay rates for a σ-evolution equation in Rn under effects of a damping term represented by the action of a fractional Laplacian operator and a time-dependent coefficient, b(t)(−Δ)θut(t,x). We consider that b is ‘confined’ in the curve g(t)=(1+t)αlnγ(1+t) for large t⩾t0 and without any control on ddtb(t).

Keywords: Wave equation, plate equation, fractional damping, sharp decay rates, non-effective damping, multiplier method

DOI: 10.3233/ASY-191566

Journal: Asymptotic Analysis, vol. 119, no. 1-2, pp. 61-86, 2020