Displaying similar documents to “Global solutions to some nonlinear dissipative mildly degenerate Kirchhoff equations.”

One-dimensional model describing the non-linear viscoelastic response of materials

Tomáš Bárta (2014)

Commentationes Mathematicae Universitatis Carolinae


In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.

Decay rates of Volterra equations on ℝN

Monica Conti, Stefania Gatti, Vittorino Pata (2007)

Open Mathematics


This note is concerned with the linear Volterra equation of hyperbolic type t t u ( t ) - α Δ u ( t ) + 0 t μ ( s ) Δ u ( t - s ) d s = 0 on the whole space ℝN. New results concerning the decay of the associated energy as time goes to infinity were established.