Displaying similar documents to “Well-posedness results for a model of damage in thermoviscoelastic materials”

Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials

Elisabetta Rocca, Riccarda Rossi (2008)

Applications of Mathematics

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This paper is devoted to the analysis of a one-dimensional model for phase transition phenomena in thermoviscoelastic materials. The corresponding parabolic-hyperbolic PDE system features a internal energy balance equation, governing the evolution of the absolute temperature ϑ , an evolution equation for the phase change parameter χ , including constraints on the phase variable, and a hyperbolic stress-strain relation for the displacement variable 𝐮 . The main novelty of the model is that...

On a conserved Penrose-Fife type system

Gianni Gilardi, Andrea Marson (2005)

Applications of Mathematics

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We deal with a class of Penrose-Fife type phase field models for phase transitions, where the phase dynamics is ruled by a Cahn-Hilliard type equation. Suitable assumptions on the behaviour of the heat flux as the absolute temperature tends to zero and to + ∞ are considered. An existence result is obtained by a double approximation procedure and compactness methods. Moreover, uniqueness and regularity results are proved as well.

An elastic membrane with an attached non-linear thermoelastic rod

Werner Horn, Jan Sokołowski (2002)

International Journal of Applied Mathematics and Computer Science

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We study a thermo-mechanical system consisting of an elastic membrane to which a shape-memory rod is glued. The slow movements of the membrane are controlled by the motions of the attached rods. A quasi-static model is used. We include the elastic feedback of the membrane on the rods. This results in investigating an elliptic boundary value problem in a domain Ω ⊂ R^2 with a cut, coupled with non-linear equations for the vertical motions of the rod and the temperature on the rod. We...

One-dimensional model describing the non-linear viscoelastic response of materials

Tomáš Bárta (2014)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.