Author
Ball, J. M., Şengül, Yasemin
Publication Date
2014
Publication Place
-
Springer Science+Business Media
Subject
Viscoelasticity, Gradient flows, Nonlinear partial differential equations, Infinite-dimensional dynamical systems
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
1572-9222
Record ID
a8140187-8c0b-4667-9cfb-5a2538f46981
Library Location
Natural and Mathematical Sciences
Date
2014
Notes
Oxford Centre for Nonlinear PDE ; European Commission ; TÜBİTAK
Sample Text
We consider the equation of motion for one-dimensional nonlinear viscoelasticity of strain-rate type under the assumption that the stored-energy function is λ-convex, which allows for solid phase transformations. We formulate this problem as a gradient flow, leading to existence and uniqueness of solutions. By approximating general initial data by those in which the deformation gradient takes only finitely many values, we show that under suitable hypotheses on the stored-energy function the deformation gradient is instantaneously bounded and bounded away from zero. Finally, we discuss the open problem of showing that every solution converges to an equilibrium state as time t→∞ and prove convergence to equilibrium under a nondegeneracy condition. We show that this condition is satisfied in particular for any real analytic cubic-like stress-strain function.
DOI
10.1007/s10884-014-9410-1
