Apparition éventuelle de singularités dans des problèmes d'évolution non linéaires

 Access to full text

 Full (PDF)

1. [1] C. Bardos et U. Frisch - Finite time regularity for bounded and unbounded ideal incompressible fluid. Turbulence and Navier stokes equation, Springer-Verlag Lecture Notes, n° 565 (ed. R. Temam). Zbl0355.76016MR467034
2. [2] J. Chadam - Asymptotics for Du = m2u+G(x,t,u,ux,ut) Global existence and Decay, Annali della scuola Norm. Sup. di Pisa, Vol. 26(1972), 31-65. Zbl0241.35014
3. [3] H. Fujita - On the blowing up of solutions of the Cauchy problem for ut = Δu+n1+α, J. Fac. Sci. Univ. Tokyo, sect. 1, 13(1966), 109-124. Zbl0163.34002
4. [4] R. Glassey - On the blowing up of solution to the Cauchy problem for the non linear Schrödinger equation, J. Math. Phys., 18(1977), 1794-1799. Zbl0372.35009MR460850
5. [5] J. Ginibre et G. Velo - On a class of non linear equations, (to appear). 
6. [6] L. Hormander - Implicit function theorem, Lectures at Stanford Univ., Eté 1977. 
7. [7] F. John - Blow up of solution of non linear wave equations in three space dimensions, Manuscripta Math., 28(1979), 235-268. Zbl0406.35042MR535704
8. [8] F. John - Formation of singularities in one dimensional non linear wave propagation, Com. Pure Appl. Math., 27(1974), 377-405. Zbl0302.35064MR369934
9. [9] S. Klainerman - Global existence for non linear wave equations, Comm. Pure Appl. Math., 33(1980), 43-101. Zbl0405.35056MR544044
10. [10] S. Klainerman - Long time behaviour of solutions to non linear evolution equations, preprint. 
11. [11] S. Klainerman et A. Majda - Formation of singularities for wave equations including the non linear vibrating string, preprint. 
12. [12] P. Lax - Hyperbolic systems of conservation laws and the mathematical theory of shock waves, Regional Conference Serie in Applied Math., SIAM, 1973. Zbl0268.35062MR350216
13. [13] R. Morf, S. Orzag et U. Frisch - Spontaneous singularity in three dimensional inviscid, incompressible flow, Phys. Review Letters, Vol. 44, n° 9(1980), 572-575. MR558166
14. [14] J. Moser - A new technique for the construction of solution of non linear differential equations, Proc. Natl. Acad. Sci. USA, 47(1961), 1824-1831. Zbl0104.30503MR132859
15. [15] J. Nash - The embedding problem for Riemannian manifolds, Ann. Math., 63(1956), 20-63. Zbl0070.38603MR75639
16. [16] W. Strauss - Non linear scattering theory, Scattering theory in Math. Phys.53-78, La Vita et Marchand (eds) D. Reidel (1974). Zbl0297.35062
17. [17] V.E. Zakharov et A.B. Shabat - Exact theory of two dimensional self focusing and one dimensional self modulation of waves in non linear media, J. Exp. and Th. Phys., 61(1971), 118-134. MR406174
18. [18] R. Glassey - Finite-time blow up for solutions of non linear wave equations, preprint. 
19. [19] T.P. Liu - Development of singularities in the non linear waves for quasilinear hyperbolic partial differential equations, J. Diff. Eq., 33(1979), 92-111. Zbl0379.35048MR540819

1. Bruno Sevennec, Géométrie des systèmes hyperboliques de lois de conservation