SHARP TIME DECAY RATES ON A HYPERBOLIC PLATE MODEL UNDER EFFECTS OF AN INTERMEDIATE DAMPING WITH A TIME-DEPENDENT COEFFICIENT

Author(s)

D'Abbicco, Marcello ^[1] ; Charao, Ruy Coimbra ^[2] ; da Luz, Cleverson Roberto ^[2]

Affiliation

^[1] Univ Sao Paulo, FFCLRP, Dept Comp & Matemat, BR-14040901 Ribeirao Preto, SP - Brazil

^[2] Univ Fed Santa Catarina, Dept Math, BR-88040900 Florianopolis, SC - Brazil

• Document type: Journal article
• Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 36, n. 5, p. 2419-2447, MAY 2016.
• Web of Science Citations: 1

Abstract

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 (-Delta)(theta), in the damping term, theta is an element of {[}0, 1]. For the special time-dependent coefficient b (t) = mu (1+ t)(alpha), alpha is an element of (0, 1], we get optimal decay rates (Theorem 3.1, Section 3). (AU)

• FAPESP's process: 13/15140-2 - Decay estimates for semilinear hyperbolic equations
• Grantee: Marcello Dabbicco
• Support Opportunities: Research Grants - Young Investigators Grants
• FAPESP's process: 14/02713-7 - Decay estimates for semilinear hyperbolic equations
• Grantee: Marcello Dabbicco
• Support Opportunities: Scholarships in Brazil - Young Researchers