Asymptotic behavior of a class of abstract semilinear integrodifferential equations and applications. (English) Zbl 0981.45007
Summary: A class of semilinear hyperbolic Volterra integrodifferential equations in Hilbert spaces is considered. The main results in this paper are the global existence of solutions to the initial problem of the equation for large data and an asymptotic estimation of the solution. An application to a system relating to three-dimensional viscoelastic dynamics is presented.
MSC:
| 45K05 | Integro-partial differential equations |
| 45M05 | Asymptotics of solutions to integral equations |
| 74D10 | Nonlinear constitutive equations for materials with memory |
| 45N05 | Abstract integral equations, integral equations in abstract spaces |
Keywords:
semilinear hyperbolic Volterra integrodifferential equations; Hilbert spaces; global existence; initial problem; asymptotic; viscoelastic dynamicsReferences:
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