Weak solutions for a class of nonlinear systems of viscoelasticity

Archive for Rational Mechanics and Analysis

Volumn 155, Issue 4, 2000, Pages 299-334

  Demoulini, Sophia ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034550804     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050000115     Document Type: Article

References (30)

1. x, J. Diff. Eqs. 35, 200-231, 1980.
2. G. ANDREWS & J. BALL, Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity, J. Diff. Eqs. 44, 306-341, 1982.
3. S. ANTMAN, Nonlinear problems in elasticity, Applied Mathematical Sciences, Vol. 107, Springer Verlag, New York 1995.
4. S. ANTMAN & T. SEIDMAN, Quasilinear Hyperbolic-Parabolic Equations of One-Dimensional Viscoelasticity, J. Diff. Eqs. 124, 132-184, 1996.
5. S. ANTMAN, Physically unacceptable viscous stresses, Z. Angew. Math. Phys. 49, 980-988, 1998.
6. S. ANTMAN & H. KOCH, Self-sustained oscillations of nonlinearly viscoelastic layers. To appear.
7. J. BALL, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63, 337-403. 1977.
8. J. BALL, B. KIRCHHEIM & J. KRISTENSEN, Regularity of quasiconvex envelopes. Preprint.
9. P. CIARLET, Mathematical Elasticity, Vol. 1: Three-Dimensional Elasticity, Studies in Mathematics and Its Appliations, Vol. 20, North-Holland, Amsterdam 1994.
10. B. COLEMAN & W. NOLL, On the Thermostatics of Continuous Media, Arch. Rational Mech. Anal. 4, 97-128, 1959.
11. C. DAFERMOS, The mixed initial-boundary value problem for the equations of one-dimensional nonlinear viscoelasticity, J. Diff. Eqs. 6, 71-86, 1969.
12. C. DAFERMOS, Hyperbolic Conservation Laws in Continuum Physics, Springer Verlag, New York 2000.
13. S. DEMOULINI, Young measure solution for a nonlinear parabolic equation of forward-backward type, SIAM J. Math. Anal. 27, 376-403, 1996.
14. S. DEMOULINI, Young measure solutions for nonlinear evolutionary systems of mixed type, Ann. Inst. Henri Poincaré, Analyse non linéaire, 14, 143-162, 1997.
15. S. DEMOULINI, D. STUART & A. TZAVARAS, Construction of entropy solutions for one-dimensional elastodynamics via time discretisation, Ann. Inst. Henri Poincaré. Analyse non linéaire 17, 711-731, 2000
16. S. DEMOULINI, D. STUART & A. TZAVARAS, A variational approximation scheme for three dimensional elastodynamics with polyconvex energy. Arch RAtional Mechn. Anal., to appear
17. L. EVANS, Weak convergence methods for nonlinear partial differential equations, CBMS Vol 74, American Mathematical Society, Providence 1990.
18. G. FRIESECKE & G. DOLZMANN, Implicit time discretization and global existence for a quasilinear evolution equation with nonconvex energy, SIAM J. Math. Anal. 28, 363-380, 1997.
19. C. HAMBURGER, Quasimonotonicty, regularity and duality for nonlinear sytems of partial differential equations. Annali Mat. pura ed appl. 69, 321-354, 1995.
20. D. KINDERLEHRER & P. PEDREGAL, Weak convergence of integrands and the Young measure representation, SIAM J. Math. Anal. 23, 1-19, 1992.
21. D. KINDERLEHRER & P. PEDREGAL, Gradient Young measures generated by sequences in Sobolev spaces, J. Geom. Anal. 4, 59-90 1994.
22. R. LANDES, Quasimonotone versus pseudomonotone. Proc. Roy. Soc. Edin. A 126, 705-717, 1996.
23. J. L. LIONS, Quelques Méthodes de résolution des problemes aux limites non linéaires. Études Mathématiques, Dunod, Paris 1969.
24. J. MARSDEN & T. HUGHES, Mathematical Foundations of Elasticity, (Prentice-Hall, 1983) Dover, New York 1993.
25. R. PEGO, Phase transitions in one-dimensional nonlinear viscoelasticity, Arch. Rational Mech. Anal. 97, 353-394, 1987.
26. M. POTIER-FERRY, On the Mathematical Foundations of Elastic Stability Theory.I. Arch. Rational Mech. Anal. 78, 55-72, 1982.
27. P. RYBKA, Dynamical modeling of phase transitions by means of viscoelasticity in many dimensions, Proc. Roy. Soc. Edin. A 121, 101-138, 1992.
28. L. TARTAR, Compensated compactness and partial differential equations. In Nonlinear Analysis and Mechanics, KNOPS, ed., Vol. IV, Pitman Research Notes in Mathematics, 1979, pp. 136-212.
29. E. ZEIDLER, Nonlinear Functional Analysis and Its Applications II A, Springer Verlag, New York 1990.
30. K.-W. ZHANG, On the Dirichlet problem for a class of quasilinear elliptic systems of partial differential equations in divergence form, Chern, ed., Vol. 1306, Springer Lecture Notes in Mathematics 1988, pp. 262-277.