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- Title
New general decay result for a system of two singular nonlocal viscoelastic equations with general source terms and a wide class of relaxation functions.
- Authors
Al-Gharabli, Mohammad M.; Al-Mahdi, Adel M.; Messaoudi, Salim A.
- Abstract
This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumption on the behavior of the relaxation function k i , namely, k i ′ (t) ≤ − ξ i (t) Ψ i (k i (t)) , i = 1 , 2. We establish a new general decay result that improves most of the existing results in the literature related to this system. Our result allows for a wider class of relaxation functions, from which we can recover the exponential and polynomial rates when k i (s) = s p and p covers the full admissible range [ 1 , 2) .
- Subjects
EQUATIONS; MATHEMATICAL decomposition; CONVEX functions
- Publication
Boundary Value Problems, 2020, Vol 2020, Issue 1, pN.PAG
- ISSN
1687-2762
- Publication type
Article
- DOI
10.1186/s13661-020-01467-5