Open AccessGlobal existence and energy decay of a nondissipative Cauchy viscoelastic problem
Author(s) -
Mohammad Kafini,
Muhammad I. Mustafa
Publication year - 2015
Publication title -
quarterly of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.603
H-Index - 41
eISSN - 1552-4485
pISSN - 0033-569X
DOI - 10.1090/qam/1420
Subject(s) - dissipative system , infinity , initial value problem , viscoelasticity , mathematics , mathematical analysis , term (time) , polynomial , cauchy problem , nonlinear system , kernel (algebra) , cauchy distribution , zero (linguistics) , energy method , space (punctuation) , physics , pure mathematics , computer science , quantum mechanics , linguistics , philosophy , operating system , thermodynamics
A viscoelastic Cauchy problem subjected to a nonlinear source term is investigated. The memory term in the system involves a kernel which is regular, as is usually the case, but the system is not dissipative and is considered in the whole space. We prove global existence and nonexistence results. In the case of global existence, we show that solutions go to zero in a polynomial manner as time goes to infinity under some conditions on the source.