Local Analyticity in Weighted L 1 -Spaces and Applications to Stability Problems for Volterra Equations

Jordan, G. S.; Staffans, Olof J.; Wheeler, Robert L.

doi:10.2307/1999131

Cited by 11 publications

(11 citation statements)

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“…If we assume that b = 0, t2m(t) e L'(0, oo), and initial conditions (1.3b) hold, then it follows from Proposition 2.3 of [16] and some routine computations that J*, /'* e L'(0, oo), and consequently J*(t) -> 0 as t -» oo, i.e. J(t) -> -(/0°° ™(t) Jt)"1 as t -* oo.…”

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confidence: 99%

On wave propagation in linear viscoelasticity

Hrusa¹,

Renardy²

1985

Quart. Appl. Math.

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Abstract. We discuss the initial value problem in one-dimensional linear visco-elasticity with a step-jump in the initial data. If the memory kernel is sufficiently smooth on [0 , oo), the solution exhibits discontinuities propagating along characteristics and a (higher order) stationary discontinuity at the position of the original step-jump. For a singular memory kernel, the propagating waves are smoothed in a manner depending on the nature of the singularity in the kernel, but the stationary discontinuity remains. We also discuss the effects of these phenomena on the regularity of solutions with arbitrary initial data.

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confidence: 99%

On wave propagation in linear viscoelasticity

Hrusa¹,

Renardy²

1985

Quart. Appl. Math.

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“…There exists GEC "x" such that X(t)- We remark that the structure of solutions of (1) was widely studied by many authors in very general situations (e.g. [3,4,5]). However, these results specialized to equation (1) Thus, it is sufficient to give a criterion for the boundedness of X(t) in order to have a complete characterization of the stability of the zero solution of (1).…”

Section: X(o) = E X'(t) = Ax(t)+(bx)(t) (T ~= O X(t)ec"•mentioning

confidence: 99%

A stability criterion for a linear Volterra equation of convolution type

Terjéki¹

1990

Acta Math Hung

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“…We call ß invertible at infinity (with respect to p), if [detp]"1 is pseudo-locally analytic at infinity in the sense of Definition 8.1 in [4]. If ß is invertible at infinity with respect to p, then necessarily (2.9) liminf |det p(z)| > 0.…”

Section: Lx(t) = X'(t) + F A(t -S)x(s) Ds ((Er)mentioning

confidence: 99%

“…Again, sufficient conditions for the existence of the dominating functions p+ and p_ are given in [4,8]. This time we have two fundamental solutions of (1.1), r+ and r_, corresponding to p+ and p_.…”

Section: U-oo Usrezmentioning

confidence: 99%