Young-measure solutions for a viscoelastically damped wave equation with nonmonotone stress-strain relation

Archive for Rational Mechanics and Analysis

Volumn 144, Issue 1, 1998, Pages 47-78

  Theil, Florian ^a  

^a Leibniz Universität Hannover   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032342276     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050112     Document Type: Article

References (21)

1. x. J. Diff. Eqns. 35, 200-231, 1980.
2. A. AMBROSETTI & G. PRODI: A Primer to Nonlinear Analysis. Cambridge University Press 1993.
3. E. J. BALDER: Consequences of denseness of Dirac Young measures. Math. Anal. Appl. 207, 536-540 (1997).
4. J. M. BALL: A version of the fundamental theorem for Young measures. Partial differential equations and continuum models of phase transitions. M. RASCLE, D. SERRE & M. SLEMROD (eds.), Springer Lecture Notes in Physics 344, 207-215 (1989).
5. J. M. BALL, P. J. HOLMES, R. D. JAMES, R. L. PEGO & P. J. SWART: On the Dynamics of Fine Structure. J. Nonlinear Sci. 1, 17-70 (1991).
6. R. J. DIPERNA: Measure-valued solutions to conservation laws. Arch. Rational Mech. Anal. 88, 223-270 (1985).
7. R. M. DUDLEY: Real Analysis and Probability. Wadsworth & Brooks/Cole, 1989.
8. R. E. EDWARDS: Functional Analysis. Holt, Rinehart and Winston, 1965.
9. I. FONSECA, D. BRANDON, & P. SWART: Dynamics and oscillatory microstructure in a model of displacive phase-transformations. Progress in Partial Differential Equations: The Metz Surveys 3. M. CHIPOT et. al. (eds.), 130-144, Longman, 1994.
10. G. FRIESECKE & J. B. MCLEOD: Dynamics as a mechanism preventing the formation of finer and liner microstructure. Arch. Rational Mech. Anal. 133, 199-247 (1996).
11. D. HENRY: Geometric Theory of Semilinear Parabolic Equations. Springer, 1981.
12. J. L. JOLY & G. MÉTEVIER & J. RAUCH: Trilinear compensated compactness and nonlinear geometric optics. Ann. Math. 142, 121-169(1995).
13. p-Young measures. Math. Anal. Appl. 198, 830-843 (1996).
14. A. MIELKE: Evolution equations for Young-measure solutions of semilinear hyperbolic problems. To appear in Proc. Roy. Soc. Edin., 1998.
15. A. PAZY: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, 1983.
16. R. L. PEGO: Phase transitions in one-dimensional viscoelasticity: Admissibility and stability. Arch. Rational Mech. Anal. 97, 353-394 (1987).
17. S. T. RACHEV: Probability Metrics and the Stability of Stochastic Models. Wiley, 1991.
18. P. J. SWART & P. J. HOLMES: Energy minimization and the formation of microstructure in dynamic anti-plane shear. Arch. Rational Mech. Anal. 121, 37-85 (1992).
19. L. TARTAR: Oscillations and asymptotic behavior of two semilinear hyperbolic systems. Dynamics of Infinite Dimensional Systems. S. N. CHOW & J. K. HALE (eds.), 341-356, Springer, 1987.
20. L. TARTAR: Solutions oscillantes des équations de Carleman. Goulaouic-Meyer-Schwartz Seminar Exp. No. XII, 15pp, 1981.
21. F. THEIL: Young-measure solutions for a microkinetically regularized wave equation (Draft). Universität Hannover, 1996.