Variational formulation and asymptotic analysis of viscoelastic problem with Riemann‐Liouville fractional derivatives. (26th July 2019)

• Record Type: Journal Article
• Authors: Dilmi, Mohamed; Dilmi, Mourad; Benseridi, Hamid
• Other Names: Kirane Mokhtar guestEditor.; Srivastava Hari M. guestEditor.; Zhou Yong guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 3(2021)
• Page Start: 2294
• Page End: 2313
• Publication Date: 2019-07-26
• Subjects: asymptotic analysis -- fractional derivatives -- Riemann‐Liouville fractional derivatives -- Tresca law -- variational formulation -- viscoelastic problem; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5775
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we study the variational formulation and asymptotic analysis of a viscoelastic problem with fractional derivative in the Riemann‐Liouville sense and nonlinear friction of Tresca type in a three‐dimensional thin domain Ω ε . We prove the existence and uniqueness of the weak solution; then, we study the asymptotic analysis when one dimension of the domain tends to zero. The limit problem, the limit of Tresca free boundary conditions, and the specific Reynolds equation are obtained.