A Cauchy problem for the Tartar equation

Royal Society of Edinburgh - Proceedings A

Volumn 132, Issue 2, 2002, Pages 395-418

  Sazhenkov, Sergey ^a  

^a LAVRENTYEV INSTITUTE OF HYDRODYNAMICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036974328     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500001700     Document Type: Conference Paper

References (32)

1. S. N. Antontsev, A. V. Kazhikhov and V. N. Monakhov. Boundary value problems in mechanics of nonhomogeneous fluids (Amsterdam: North-Holland, 1990).
2. N. Bourbaki. Livre VI. Intégration (Paris: Hermann, 1965).
3. R. Courant and D. Hilbert. Methods of mathematical physics, vol. II (Wiley, 1962).
4. B. Desjardins. A few remarks on ordinary differential equations. Commun. PDEs 21 (1996), 1667-1703.
5. R. J. DiPerna. Measure-valued solutions to conservation laws. Arch. Ration. Mech. Analysis 88 (1985), 223-270.
6. R. J. DiPerna and P. L. Lions. Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98 (1989), 511-547.
7. Weinan B. Homogenization of linear and nonlinear transport equations. Commun. Pure Appl. Math. 14 (1992), 301-326.
8. R. E. Edwards. Fourier series. A modern introduction, vol. 1 (Springer, 1979).
9. C. Foias, C. Guillopé and R. Temám. Lagrange representation of a flow. J. Diff. Eqns 57 (1985), 440-449.
10. P. Gerárd. Microlocal defect measures. Commun. PDEs 16 (1991), 1761-1794.
11. E. Kamke. Differentialgleichungen, Lösungmethoden und Lösungen (Leipzig: Geest and Portig, 1956).
12. L. V. Kantorovich and G. P. Akilov. Functional analysis (Moscow: Nauka, 1984). (In Russian.)
13. T. Kato. On classical solution of the two-dimensional nonstationary Euler equations. Arch. Ration. Mech. Analysis 25 (1967), 188-200.
14. 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).
15. J. Málek, J. Nečas, M. Rokyta and M. Růžička. Weak and measure-valued solutions to evolutionary PDEs (London: Chapman and Hall, 1996).
16. A. Mielke. Flow properties for Young-measure solutions of semilinear hyperbolic problems. Proc. R. Soc. Edinb. A 129 (1999), 85-123.
17. E. Yu. Panov. On sequences of measure-valued solutions to quasilinear equation of first order. Mat. USSR Sb. 185 (1994), 87-106. (In Russian.)
18. E. Yu. Panov. On strong precompactness of bounded sets of measure-valued solutions to quasilinear equation of first order. Mat. USSR Sb. 186 (1995), 103-114. (In Russian.)
19. E. Yu. Panov. On a condition for strong precompactnees of bounded sets of measure-valued solutions to quasilinear equation of first order. Mat. USSR Sb. 190 (1999), 109-128. (In Russian.)
20. L. Ryzhik, G. Papanicolaou and J. B. Keller. Transport equations for elastic and other waves in random media. Wave Motion 24 (1996), 327-370.
21. G. Sansone. Equazioni differenziali nel campo reale. Parte Prima (Bologna, 1948).
22. S. A. Sazhenkov. Solutions of a problem on motion of a viscous incompressible fluid with oscillatory initial data. Dinamika Sploshnoi Sredy: Sb. nauch. tr./Russ. Acad. Sci. Siberian Branch 113 (1998), 123-134. (In Russian.)
23. I. N. Sneddon. Elements of partial differential equations (McGraw-Hill, 1957).
24. L. Tartar. The compensated compactness method applied to systems of conservation laws. In Systems of nonlinear PDEs (ed. J. M. Ball), pp. 263-285 (Dordrecht: Reidel, 1983).
25. L. Tartar. Oscillations and asymptotic behaviour of two semilinear hyperbolic systems. In Dynamics of infinite-dimensional systems (ed. S. N. Crow and J. K. Hale), pp. 341-356 (Springer, 1987).
26. L. Tartar. H-measures, a new approach for studying homogenisation oscillations and concentration effects in partial differential equations. Proc. R. Soc. Edinb. A 115 (1990), 193-230.
27. L. Tartar. On mathematical tools for studying partial differential equations of continuum physics: H-measures and Young measures. In Developments in partial differential equations and applications to mathematical physics (ed. G. Butazzo, G. P. Galdi and L. Zanghirati), pp. 201-207 (New York: Plenum, 1992).
28. C. Truesdell. A first course in rational continuum mechanics (Baltimore, MD: Johns Hopkins University, 1972).
29. V. S. Vladimirov. Equations of mathematical physics (Moscow: Nauka, 1981). (In Russian.)
30. J. Warga. Optimal control of differential and functional equations (Academic, 1972).
31. E. Wigner. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40 (1932), 749-759.
32. L. C. Young. Lectures on the calculus of variations and optimal control theory (Philadelphia, PA: Saunders, 1969).