Open AccessSharp time decay rates on a hyperbolic plate model under effects of an intermediate damping with a time-dependent coefficient
Author(s) -
Marcello D’Abbicco,
Ruy Coimbra Charão,
Cleverson Roberto da Luz
Publication year - 2015
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2016.36.2419
Subject(s) - exponent , physics , operator (biology) , mathematical analysis , fractional laplacian , laplace operator , term (time) , exponential decay , mathematical physics , work (physics) , section (typography) , mathematics , quantum mechanics , philosophy , linguistics , biochemistry , chemistry , repressor , transcription factor , gene , advertising , business
In this work we study decay rates for a hyperbolic plate equation under effects of an intermediate damping term represented by the action of a fractional Laplacian operator and a time-dependent coefficient. We obtain decay rates with very general conditions on the time-dependent coefficient (Theorem 2.1, Section 2), for the power fractional exponent of the Laplace operator (-Δ)θ, in the damping term, θ ∈ [0, 1]. For the special time-dependent coefficient b(t) = μ(1+t)α, α ∈ (0, 1], we get optimal decay rates (Theorem 3.1, Section 3)