Solutions in the large for certain nonlinear parabolic systems

David Hoff; Joel Smoller

Annales de l'I.H.P. Analyse non linéaire (1985)

  • Volume: 2, Issue: 3, page 213-235
  • ISSN: 0294-1449

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Hoff, David, and Smoller, Joel. "Solutions in the large for certain nonlinear parabolic systems." Annales de l'I.H.P. Analyse non linéaire 2.3 (1985): 213-235. <http://eudml.org/doc/78097>.

@article{Hoff1985,
author = {Hoff, David, Smoller, Joel},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {global existence; smooth solutions; local solution; entropy-entropy flux; gas dynamics; Navier-Stokes equations},
language = {eng},
number = {3},
pages = {213-235},
publisher = {Gauthier-Villars},
title = {Solutions in the large for certain nonlinear parabolic systems},
url = {http://eudml.org/doc/78097},
volume = {2},
year = {1985},
}

TY - JOUR
AU - Hoff, David
AU - Smoller, Joel
TI - Solutions in the large for certain nonlinear parabolic systems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1985
PB - Gauthier-Villars
VL - 2
IS - 3
SP - 213
EP - 235
LA - eng
KW - global existence; smooth solutions; local solution; entropy-entropy flux; gas dynamics; Navier-Stokes equations
UR - http://eudml.org/doc/78097
ER -

References

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  2. [2] K. Chueh, C. Conley and J. Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Ind. U. Math. J., t. 26, 1977, p. 373-392. Zbl0368.35040MR430536
  3. [3] R. Courant and K.O. Friedrichs, Supersonic Flow and Shock Waves, Wiley-InterscienceNew York, 1948. Zbl0041.11302MR29615
  4. [4] D. Hoff, Invariant regions and finite difference schemes for systems of conservation laws, Trans. Amer. Math. Soc. (to appear). Zbl0535.35056MR784005
  5. [5] D. Hoff and J. Smoller, Error bounds for finite difference approximations for a class of nonlinear parabolic systems, Math. Comp. (to appear). Zbl0613.65096MR790643
  6. [6] N. Itaya, On the Cauchy problem for the system of fundamental equations describing the movement of a compressible fluid, Kodai Math. Sem. Rep., t. 23, 1971, p. 60-120. Zbl0219.76080MR283426
  7. [7] Ya. Kanel', On some systems of quasilinear parabolic equations, USSR Comp. Math. and Math. Phys., t. 6, 1966, p. 74-88. Zbl0157.17401
  8. [8] Ya. Kanel', On a model system of equations of one-dimensional gas motion, Diff. Equs., t. 4, 1968, p. 374-380. Zbl0235.35023
  9. [9] S. Kawashima and T. Nishida, The initial-value problems for the equations of a viscous compressible and perfect compressible fluids, RIMS, Kokyunoku 428, Kyoto Univ., Nonlinear Functional Analysis, June 1981, p. 34-59. 
  10. [10] A. Kazhikov and V. Shelukhin, Unique global solution in time of initial-boundary-value problems for one dimensional equations of a viscous gas. P. M. M. J. Appl. Math. Mech., t. 41, 1977, p. 273-281. Zbl0393.76043MR468593
  11. [11] O.A. Ladyzenskaya, V.A. Solonnikov and N.N. Uraltseva, Linear and Quasi-linear Equations of Parabolic Type, Amer. Math. Soc. Translation, Providence, 1968. Zbl0174.15403
  12. [12] P. Lax, Shock waves and entropy, in Contributions to NonlinearFunctional Analysis, ed. by E. Zaratonello, Acad. Press, New York, 1971, p. 603-634. Zbl0268.35014MR393870
  13. [13] A. Matsumura and T. Nishida, The initial-value problem for the equations of motion of viscous and heat conductive gases, J. Math. Kyoto Univ., t. 20, 1980, p. 67-104. Zbl0429.76040MR564670
  14. [14] T. Nishida and J. Smoller, A class of convergent finite difference schemes for certain nonlinear parabolic systems. Comm. Pure Appl. Math., t. 36, 1983, p. 785-808. Zbl0535.65063MR720594
  15. [15] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer Verlag: New York, 1983. Zbl0508.35002MR688146
  16. [16] Ding Xiaxi and Wang Jinghua, Global solutions for a semilinear parabolic system, Acta. Math. Scientia, t. 3, 1983, p. 397-414. Zbl0592.65056

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