Quasistatic nonlinear viscoelasticity and gradient flows

Article, Preprint English OPEN
Ball, J. M.; Şengül, Yasemin;
  • Publisher: Springer Science+Business Media
  • Related identifiers: doi: 10.1007/s10884-014-9410-1
  • Subject: Nonlinear partial differential equations | Viscoelasticity | Mathematics - Analysis of PDEs | Gradient flows | Infinite-dimensional dynamical systems | 35A01, 35A02, 74D10, 82B26

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 ... View more
  • References (31)
    31 references, page 1 of 4

    [Aaronson, 1997] Aaronson, J. (1997). An Introduction to In nite Ergodic Theory, volume 50 of Mathematical Surveys and Monographs. American Mathematical Society.

    [Ambrosio et al., 2005] Ambrosio, L., Gigli, N., and Savare, G. (2005). Gradient ows : in metric spaces and in the space of probability measures. Boston : Birkhuser.

    [Andrews, 1979] Andrews, G. (1979). On the existence and asymptotic behaviour of solutions to a damped nonlinear wave equation. Thesis, Heriot-Watt University.

    [Andrews, 1980] Andrews, G. (1980). On the existence of solutions to the equation utt = uxxt + (ux)x. Journal of Di erential Equations, 35:200{231.

    [Andrews and Ball, 1982] Andrews, G. and Ball, J. M. (1982). Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity. Journal of Di erential Equations, 44:306{341.

    [Antman and Seidman, 1996] Antman, S. S. and Seidman, T. I. (1996). Quasilinear hyperbolicparabolic equations of one-dimensional viscoelasticity. Journal of Di erential Equations, 124:132{185.

    [Antman and Seidman, 2005] Antman, S. S. and Seidman, T. I. (2005). The parabolichyperbolic system governing the spatial motion of nonlinearly viscoelastic rods. Arch. Ration. Mech. Anal., 175(1):85{150.

    [Ball, 1997] Ball, J. M. (1997). Continuity properties and global attractors of generalized semi ows and the Navier-Stokes equations. Journal of Nonlinear Science, 7:475{502.

    [Ball et al., 1991] Ball, J. M., Holmes, P. J., James, R. D., Pego, R. L., and Swart, P. J. (1991). On the dynamics of ne structure. J. Nonlinear Sci., 1:17{70.

    [Crandall and Pazy, 1969] Crandall, M. G. and Pazy, A. (1969). Semi-groups of nonlinear contractions and dissipative sets. J. Funct. Anal., 3:376{418.

  • Similar Research Results (1)
  • Related Organizations (4)
  • Metrics
Share - Bookmark