Existence and uniform decay for a non‐linear viscoelastic equation with strong damping | Zendy

Cavalcanti M. M. | Zendy; Domingos Cavalcanti V. N. | Zendy; Ferreira J. | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Existence and uniform decay for a non‐linear viscoelastic equation with strong damping

Author(s) -

Cavalcanti M. M.,

Domingos Cavalcanti V. N.,

Ferreira J.

Publication year - 2001

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.250

Subject(s) - viscoelasticity , mathematics , relaxation (psychology) , exponential growth , domain (mathematical analysis) , mathematical analysis , exponential decay , function (biology) , energy (signal processing) , energy method , physics , thermodynamics , statistics , quantum mechanics , psychology , social psychology , evolutionary biology , biology

This paper is concerned with the non‐linear viscoelastic equation$$|u_{t}|^{\rho} u_{tt} - \Delta u - \Delta u_{tt} + \int\nolimits_{0}^{t} g (t - \tau)\,\Delta u (\tau)\,{\rm{d}}\tau - \gamma \Delta u_{t} \,{=}\, 0$$We prove global existence of weak solutions. Furthermore, uniform decay rates of the energy are obtained assuming a strong damping Δ u t acting in the domain and provided the relaxation function decays exponentially. Copyright © 2001 John Wiley & Sons, Ltd.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research