We consider the equation of viscoelasticity characterized by a nonlinear elastic force φ depending on the displacement u and subject to a time dependent external load F. The dissipativity of the corresponding evolution system is only due to the presence of the relaxation kernel k. Rescaling k(s)-k(∞) with a relaxation time ε>0, we can find a sufficiently small ε_0>0, such that, if φ is real analytic and ε∈ (0,ε_0], then any sufficiently smooth u converges to a single stationary state with an algebraic decay rate, provided that F suitably converges to a time independent load.The proof relies on the well-known Łojasiewicz-Simon inequality.

Convergence to stationary states of solutions to the semilinear equation of viscoelasticity / Gatti, Stefania; Grasselli, M.. - STAMPA. - 251:(2006), pp. 131-147.

Convergence to stationary states of solutions to the semilinear equation of viscoelasticity

GATTI, Stefania;
2006

Abstract

We consider the equation of viscoelasticity characterized by a nonlinear elastic force φ depending on the displacement u and subject to a time dependent external load F. The dissipativity of the corresponding evolution system is only due to the presence of the relaxation kernel k. Rescaling k(s)-k(∞) with a relaxation time ε>0, we can find a sufficiently small ε_0>0, such that, if φ is real analytic and ε∈ (0,ε_0], then any sufficiently smooth u converges to a single stationary state with an algebraic decay rate, provided that F suitably converges to a time independent load.The proof relies on the well-known Łojasiewicz-Simon inequality.
Differential equations: inverse and direct problems, Lect.Notes Pure Appl.Math.
9781584886044
Taylor and Francis
STATI UNITI D'AMERICA
Convergence to stationary states of solutions to the semilinear equation of viscoelasticity / Gatti, Stefania; Grasselli, M.. - STAMPA. - 251:(2006), pp. 131-147.
Gatti, Stefania; Grasselli, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/461846
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