TITLE

Existence and Asymptotic Stability for Viscoelastic Evolution Problems on Compact Manifolds

AUTHOR(S)
Andrade, Doherty; Cavalcanti, Marcelo M.; Domingos Cavalcanti, Valéria N.; Portillo Oquendo, Higidio
PUB. DATE
April 2006
SOURCE
Journal of Computational Analysis & Applications;Apr2006, Vol. 8 Issue 2, p173
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
One considers the nonlinear viscoelastic evolution equation utt + Au + F(x, t, u, uT) - g * Au = 0 on Γ x (0, ∞) where Γ is a compact manifold. When F ≠ 0 and g = 0 we prove existence of global solutions as well as uniform (exponential and algebraic) decay rates. Furthermore, if F = 0 and g ≠ 0 we prove that the dissipation introduced by the memory effect is strong enough to allow us to derive an exponential( or polynomial) decay rate provided the resolvent kernel of the relaxation function decays exponentially (or polynomially).
ACCESSION #
21501450

 

Related Articles

  • The Cross Curvature Flow of 3-Manifolds with Negative Sectional Curvature. Chow, Bennett; Hamilton, Richard S. // Turkish Journal of Mathematics;2004, Vol. 28 Issue 1, p1 

    We consider the cross curvature flow, an evolution equation of metrics on 3- manifolds. We establish short time existence when the sectional curvature has a sign. In the case of negative sectional curvature, we obtain some monotonicity formulas which support the conjecture that after...

  • Steepest descent method on a Riemannian manifold: the convex case. Munier, Julien // Balkan Journal of Geometry & Its Applications;2007, Vol. 12 Issue 2, p98 

    In this paper we are interested in the asymptotic behavior of the trajectories of the famous steepest descent evolution equation on Riemannian manifolds. It writes ẋ (t) + gradϕ (x (t)) = 0. It is shown how the convexity of the objective function ϕ helps in establishing the...

  • Geometric method of reconstructing systems from experimental data. Nikulchev, E. // Technical Physics Letters;Mar2007, Vol. 33 Issue 3, p267 

    A method of reconstructing model dynamic evolution equations reduced to the central invariant manifold is described, which is based on an analysis of experimental data from controlled objects. The proposed method takes into account the group transformations of phase trajectories, which retain...

  • UNIFORM POLYNOMIAL TRICHOTOMY OF EVOLUTION OPERATORS IN BANACH SPACES. Ramneantu, Magda Luminita // Journal of Advanced Mathematical Studies;Aug2012, Vol. 5 Issue 2, p101 

    This paper presents necessary and sufficient conditions for uniform polynomial trichotomy of evolution operators in Banach spaces. Well-known results for uniform exponential trichotomy are extended to the case of uniform polynomial trichotomy.

  • CENTER-UNSTABLE MANIFOLDS FOR NONDENSELY DEFINED CAUCHY PROBLEMS AND APPLICATIONS TO STABILITY OF HOPF BIFURCATION. ZHIHUA LIU; MAGAL, PIERRE; SHIGUI RUAN // Canadian Applied Mathematics Quarterly;Summer2012, Vol. 20 Issue 2, p135 

    Center-unstable manifolds are very useful in investigating nonlinear dynamics of nonlinear evolution equations. In this paper, we first present a center-unstable manifold theory for abstract semilinear Cauchy problems with nondense domain. We especially focus on the stability property of the...

  • A simple proof on the non-existence of shrinking breathers for the Ricci flow. Hsu, Shu-Yu // Calculus of Variations & Partial Differential Equations;Sep2006, Vol. 27 Issue 1, p59 

    Suppose M is a compact n-dimensional manifold, n= 2, with a metric g ij ( x, t) that evolves by the Ricci flow ? t g ij = -2 R ij in M� (0, T). We will give a simple proof of a recent result of Perelman on the non-existence of shrinking breather without using the logarithmic Sobolev...

  • STABLE MANIFOLDS FOR NON-AUTONOMOUS EQUATIONS WITH NON-UNIFORM POLYNOMIAL DICHOTOMIES. Bento, António J. G.; Silva, César M. // Quarterly Journal of Mathematics;Jun2012, Vol. 63 Issue 2, p275 

    We establish the existence of stable manifolds for semiflows defined in Banach spaces by non-autonomous ordinary differential equations v′ = A(t)v + f(t, v) assuming that the non-autonomous linear equation v′ = A(t)v admits a type of non-uniform dichotomy that we call non-uniform...

  • Reduction of underdetermined systems of ordinary differential equations: III. Elkin, V. // Differential Equations;Nov2011, Vol. 47 Issue 11, p1556 

    We consider the problem on the restriction of underdetermined systems of ordinary differential equations linear in the derivatives to a manifold.

  • Multistability in nonlinear parabolic systems with low diffusion. Kashchenko, I. S. // Doklady Mathematics;Dec2010, Vol. 82 Issue 3, p878 

    The article studies the local dynamics of the system of nonlinear parabolic-type equations in the case where the matrices have no eigenvalues in the right complex half plane. It considers the systems of nonlinear parabolic-type equations with periodic boundary equations. It notes that known...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics