Phragmén–Lindelöf alternative of exponential type for the solutions of a fourth order dispersive equation

Quintanilla, R.; Saccomandi, Giuseppe

doi:10.4171/rlm/620

Cited by 2 publications

(2 citation statements)

References 6 publications

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“…The situation is also challenging from a mathematical point of view as it is possible to appreciate from [28] and [29], but it seems the only way to produce effective models of dissipative effects in materials subject to large deformations.…”

Section: Discussionmentioning

confidence: 99%

Spatial estimates for Kelvin–Voigt finite elasticity with nonlinear viscosity: Well behaved solutions in space

Quintanilla

Saccomandi

2020

Anal. Appl.

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We provide some spatial estimates for the nonlinear partial differential equation governing anti-plane motions in a nonlinear viscoelastic theory of Kelvin–Voigt type when the viscosity is a function of the strain rate. The spatial estimates we prove are an alternative of Phragmen–Lindelöf type. These estimates are possible when a precise balance between the elastic and viscoelastic nonlinearities holds.

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Section: Discussionmentioning

confidence: 99%

Spatial estimates for Kelvin–Voigt finite elasticity with nonlinear viscosity: Well behaved solutions in space

Quintanilla

Saccomandi

2020

Anal. Appl.

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“…It is usual to consider a semi-infinite cylinder whose finite end is perturbed and to see what happens when the spatial variable increases. We recall several spatial decay contributions for the theory of Chen et al [1,37], or more recently, for the Type II with two temperatures [42]. Our present contribution intends to overcome at least two mathematical difficulties.…”

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confidence: 96%

On the backward in time problem for the thermoelasticity with two temperatures

Leseduarte¹,

Quintanilla²

2014

Discrete &Amp; Continuous Dynamical Systems - B

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Electronic version of an article published as "Discrete and continuous dynamical series", vol. 19, no 3, May 2014, p. 679-695. DOI 10.3934/dcdsb.2014.19.679.This paper is devoted to the study of the existence, uniqueness, continuous dependence and spatial behaviour of the solutions for the backward in time problem determined by the Type III with two temperatures thermoelastodynamic theory. We first show the existence, uniqueness and continuous dependence of the solutions. Instability of the solutions for the Type II with two temperatures theory is proved later. For the one-dimensional Type III with two temperatures theory, the exponential instability is also pointed-out. We also analyze the spatial behaviour of the solutions. By means of the exponentially weighted Poincare inequality, we are able to obtain a function that defines a measure on the solutions and, therefore, we obtain the usual exponential type alternative for the solutions of the problem defined in a semi-infinite cylinder.Peer ReviewedPostprint (published version

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Phragmén–Lindelöf alternative of exponential type for the solutions of a fourth order dispersive equation

Cited by 2 publications

References 6 publications

Spatial estimates for Kelvin–Voigt finite elasticity with nonlinear viscosity: Well behaved solutions in space

Spatial estimates for Kelvin–Voigt finite elasticity with nonlinear viscosity: Well behaved solutions in space

On the backward in time problem for the thermoelasticity with two temperatures

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