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Neumann problem for one-dimensional nonlinear thermoelasticity

Yoshihiro Shibata (1992)

Banach Center Publications

The global existence theorem of classical solutions for one-dimensional nonlinear thermoelasticity is proved for small and smooth initial data in the case of a bounded reference configuration for a homogeneous medium, considering the Neumann type boundary conditions: traction free and insulated. Moreover, the asymptotic behaviour of solutions is investigated.

New methods in collision of bodies analysis

Němec, Ivan, Vala, Jiří, Štekbauer, Hynek, Jedlička, Michal, Burkart, Daniel (2023)

Programs and Algorithms of Numerical Mathematics

The widely used method for solution of impacts of bodies, called the penalty method, is based on the contact force proportional to the length of the interpenetration of bodies. This method is regarded as unsatisfactory by the authors of this contribution, because of an inaccurate fulfillment of the energy conservation law and violation of the natural demand of impenetrability of bodies. Two non-traditional methods for the solution of impacts of bodies satisfy these demands exactly, or approximately,...

New unilateral problems in stratigraphy

Stanislav N. Antontsev, Gérard Gagneux, Robert Luce, Guy Vallet (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type 0 t u - d i v { H ( t u + E ) u } , where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation...

Non linear phenomena in glaciology: ice-surging and streaming.

Emanuele Schiavi, Ana Isabel Muñoz, Ultano Kindelán (2002)

RACSAM

En estas notas presentamos algunos modelos físicos que han sido propuestos recientemente para tratar el problema de los movimientos repentinos y casi periódicos del hielo, así como la aparición de corrientes de hielo rápidas en los grandes mantos glaciares que se deslizan sobre lechos blandos y deformables. Estos fenómenos están relacionados con la transición de un régimen de flujo lento a uno rápido y pueden aparecer debido a una modificación del sistema de drenaje del glaciar. Los fenómenos en...

Non unicità dell'energia libera per materiali viscoelastici

Dario Graffi, Mauro Fabrizio (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

La non unicità dell'energia libera per un materiale viscoelastico di tipo «rate» viene provata mediante la determinazione di un controesempio.

Non-Fourier heat removal from hot nanosystems through graphene layer

A. Sellitto, F.X. Alvarez (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

Nonlocal effects on heat transport beyond a simple Fourier description are analyzed in a thermodynamical model. In the particular case of hot nanosystems cooled through a graphene layer, it is shown that these effects may increase in a ten percent the amount of removed heat, as compared with classical predictions based on the Fourier law.

Nonlinear evolution inclusions arising from phase change models

Pierluigi Colli, Pavel Krejčí, Elisabetta Rocca, Jürgen Sprekels (2007)

Czechoslovak Mathematical Journal

The paper is devoted to the analysis of an abstract evolution inclusion with a non-invertible operator, motivated by problems arising in nonlocal phase separation modeling. Existence, uniqueness, and long-time behaviour of the solution to the related Cauchy problem are discussed in detail.

Nonlinear feedback stabilization of a rotating body-beam without damping

Boumediène CHENTOUF, Jean-François COUCHOURON (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with nonlinear feedback stabilization problem of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the feedback law proposed here consists of a nonlinear control torque applied to the rigid body and either a boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends the linear...

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