Nonlinear symmetric positive systems

Kaising Tso

Annales de l'I.H.P. Analyse non linéaire (1992)

  • Volume: 9, Issue: 4, page 339-366
  • ISSN: 0294-1449

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Tso, Kaising. "Nonlinear symmetric positive systems." Annales de l'I.H.P. Analyse non linéaire 9.4 (1992): 339-366. <http://eudml.org/doc/78284>.

@article{Tso1992,
author = {Tso, Kaising},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {singular perturbation; existence; uniqueness; continuous dependence on given data; nonlinear symmetric positive system; Nash-Hörmander iteration scheme},
language = {eng},
number = {4},
pages = {339-366},
publisher = {Gauthier-Villars},
title = {Nonlinear symmetric positive systems},
url = {http://eudml.org/doc/78284},
volume = {9},
year = {1992},
}

TY - JOUR
AU - Tso, Kaising
TI - Nonlinear symmetric positive systems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1992
PB - Gauthier-Villars
VL - 9
IS - 4
SP - 339
EP - 366
LA - eng
KW - singular perturbation; existence; uniqueness; continuous dependence on given data; nonlinear symmetric positive system; Nash-Hörmander iteration scheme
UR - http://eudml.org/doc/78284
ER -

References

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  1. [1] K.O. Friedrich, Symmetric Positive Linear Differential Equations, Comm. Pure Appl. Math., Vol. 11, 1958, pp. 333-418. Zbl0083.31802MR100718
  2. [2] C. Gu, Differentiable Solutions of Symmetric Positive Partial Differential Equations, Chinese Math., Vol. 5, 1964, pp. 541-555. Zbl0222.35008MR174851
  3. [3] C. Gu, Boundary Value Problems for Quasi-linear Positive Symmetric Systems and Their Applications to Mixed Equations, Acta Math. Sinica, Vol. 21, 1978, pp. 119-129. Zbl0386.35029MR507193
  4. [4] R. Hamilton, The Inverse Function Theorem of Nash and Moser, A.M.S. Bull., Vol. 7, 1982, pp. 65-222. Zbl0499.58003MR656198
  5. [5] L. Hörmander, The Boundary Problems of Physical Geodesy, Arch. Rat. Mech. Anal., Vol. 62, 1976, pp. 1-52. Zbl0331.35020MR602181
  6. [6] S. Klainerman, Lecture Notes on Nash-Hörmander Scheme, Courant Institute. 
  7. [7] J.J. Kohn and L. Nirenberg, Non-Coercive Boundary Value Problems, Comm. Pure Appl. Math., Vol. 18, 1965, p. 443-492. Zbl0125.33302MR181815
  8. [8] P.D. Lax and R.S. Phillips, Local Boundary Conditions for Dissipative Symmetric Linear Differential Operators, Comm. Pure Appl. Math., Vol. 13, 1960, pp. 427-455. Zbl0094.07502MR118949
  9. [9] J.L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications, Vol. I, Springer-Verlag, 1972. Zbl0223.35039MR350177
  10. [10] J. Moser, A New Technique for the Construction of Solutions of Nonlinear Differential Equations, Proc. Nat. Acad. Sci., Vol. 47, 1961, pp. 1828-1831. Zbl0104.30503MR132859
  11. [11] J. Moser, A Rapidly Convergent Iteration Method and Nonlinear Differential Equations, Ann. Scuola Norm. Sup. Pisa, (3), 20, 1966, pp. 265-313. Zbl0174.47801MR199523
  12. [12] J. Nash, The Embedding Problem for Riemannian Manifolds, Ann. Math., (2), 63, 1956, pp. 20-63. Zbl0070.38603
  13. [13] P.H. Rabinowitz, A Rapid Convergence Method for a Singular Perturbation Problem, Ann. Inst. H. Poincaré Anal. Non. Linéaire, Vol. 1, 1984, pp. 1-17. Zbl0547.35047MR738493
  14. [14] L. Sarason, Differentiable Solutions of Symmetrizable and Singular Symmetric First Order Systems, Arch. Rat. Mech. Anal., Vol. 26, 1967, pp. 357-384. Zbl0162.40901MR228808
  15. [15] D. Tartakoff, Regularity of Solutions to the Boundary Value Problems for First Order Systems, Indiana Univ. Math. J., Vol. 21, 1972, pp. 1113-1129. Zbl0235.35019MR440182
  16. [16] J.C. Saut and R. Teman, Remarks on the KdV Equation, Israel J. Math., Vol. 24, 1976, pp. 78-87. Zbl0334.35062MR454425
  17. [17] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, 1977. Zbl0387.46033
  18. [18] K. Tso, A Theorem on Fully Nonlinear Degenerate Elliptic-Parabolic Equations (in preparation). 
  19. [19] J. Bona and R. Scott, Solutions of the KdV Equation in Fractional Order Sobolev Spaces, Duke Math. J., Vol. 43, 1976, pp. 87-99. Zbl0335.35032MR393887

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