Flow properties for Young-measure solutions of semilinear hyperbolic problems

Royal Society of Edinburgh - Proceedings A

Volumn 129, Issue 1, 1999, Pages 85-123

  Mielke, Alexander ^a  

^a Leibniz University Hannover   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22644452642     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500027487     Document Type: Article

References (27)

1. R. Ash. Information theory (Wiley, 1965).
2. J. M. Ball. A version of the fundamental theorem for Young measures. In Proc. of the CNRS-NSF Workshop on Continuum Theory of Phase Transitions (ed. M. Rascle, D. Serre and M. Slemrod). Springer Lecture Notes in Physics, no. 344, pp. 207-221 (Springer, 1989).
3. J. Batt. Ein Existenzbeweis für die Vlasov-Gleichung der Stellardynamik bei gemittelter Dichte. Arch. Ration. Mech. Analysis 13 (1963), 296-308.
4. S. Demoulini. Young measure solutions for a nonlinear parabolic equation of forward-backward type. SIAM J. Math. Analysis 27 (1996), 376-403.
5. R. J. DiPerna. Measure-valued solutions to conservation laws. Arch. Ration. Mech. Analysis 88 (1985), 223-270.
6. W. E and R. V. Kohn. The initial-value problem for measure-valued solutions of a canonical 2 × 2 system with linearly degenerate fields. Commun. Pure Appl. Math. 44 (1991), 981-1000.
7. I. Fonseca, D. Brandon and P. Swart. Dynamics and oscillatory microstructure in a model of displacive phase transformations. In Progress in partial differential equations: Metz surveys 3 (ed. M. Chipot, J. Saint Jean Paulin and I. Shafrir). Pitman Research Notes in Mathematics, vol. 314, pp. 130-144 (Pitman, 1994).
8. P. Gérard. Microlocal defect measures. Commun. Partial Diffl Eqns 16 (1991), 1761-1794.
9. R. T. Glassey. The cauchy problem in kinetic theory (SIAM, 1996).
10. J. L. Joly, G. Métivier and J. Rauch. Resonant one-dimensional nonlinear geometric optics. J. Functional Analysis 114 (1993), 106-231.
11. J. L. Joly, G. Métivier and J. Rauch. Trilinear compensated compactness and nonlinear geometric optics. Ann. Math. 142 (1995), 121-169.
12. F. Murat. Compacité par compensation. Ann. Sci. Norm. Sup. Pisa 5 (1978), 489-507.
13. D. McLaughlin, G. Papanicolaou and L. Tartar. Weak limits of semilinear hyperbolic systems with oscillating data. In Macroscopic modelling of turbulent flows (ed. U. Frisch, J. B. Keller, G. Papanicolaou and O. Pironneau). Springer Lecture Notes in Physics no. 230, pp. 277-289 (Springer, 1985).
14. F. Otto. Dynamics of labyrinthine pattern formation in magnetic fluids: a mean-field theory. Arch. Ration. Mech. Analysis 141 (1998), 63-103.
15. S. T. Rachev. Probability metrics and the stability of stochastic models (Wiley, 1991).
16. C. L. Siegel and J. K. Moser. Lectures on celestial mechanics. Grundlehren, vol. 187 (Springer, 1971).
17. L. Tartar. Compensated compactness and applications to PDEs. In Nonlinear mechanics and analysis (ed. R. J. Knops). Pitman Reasearch Notes in Mathematics, vol. 4, pp. 136-212 (Pitman, 1979).
18. L. Tartar. Solutions oscillantes des equations de Carleman. Seminaire Goulaouic-Meyer-Schwartz, 1980-1981, Ecole Polytechnique (Palaiseau). Expsoe XII, 1981.
19. L. Tartar. The compensated compactness method applied to systems of conservation laws. In Systems of nonlinear PDE (ed. J. M. Ball), pp. 263-285 (D. Reidel, 1983).
20. L. Tartar. Etude des oscillations dans thes equations aux derivees partielles non lineaires. In Trends in applications of pure mathematics to mechanics (ed. M. Roseau and P. G. Ciarlet). Springer Lecture Notes in Physics, no. 195, pp. 384-412 (Springer, 1984).
21. L. Tartar. Oscillations and asymptotic behaviour of two semilinear hyperbolic systems. In Dynamics of infinite dimensional systems (ed. S. N. Chow and J. K. Hale), pp. 341-356 (Springer, 1987).
22. L. Tartar, H-measures, a new approach for studying homogenisation, oscillations and concentrations effects in partial differential equations. Proc. R. Soc. Edinb. A115 (1990), 193-230.
23. L. Tartar. Oscillations for semilinear systems. Unpublished lecture notes, no. 91.3, 1991, 14 pp.
24. L. Tartar. Personal communication at Oberwolfach 1996.
25. F. Theil. Young-measure solutions for a microkinetically regularized wave equation. Draft. IfAM, Universität Hannover. September 1996.
26. F. Theil. Young measure solutions for a viscoelastically damped wave equation with non-monotone stress-strain relation. Arch. Ration. Mech. Analysis 144 (1998), 47-78.
27. F. Theil and V. I. Levitas. A Hamiltonian model for martensitic phase transformations including microkinetic energy. Math. Mech. Solids. (Submitted.)