Solutions in the large for certain nonlinear parabolic systems
Annales de l'I.H.P. Analyse non linéaire, Tome 2 (1985) no. 3, p. 213-235
@article{AIHPC_1985__2_3_213_0,
     author = {Hoff, David and Smoller, Joel},
     title = {Solutions in the large for certain nonlinear parabolic systems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {2},
     number = {3},
     year = {1985},
     pages = {213-235},
     zbl = {0578.35044},
     mrnumber = {797271},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1985__2_3_213_0}
}
Hoff, David; Smoller, Joel. Solutions in the large for certain nonlinear parabolic systems. Annales de l'I.H.P. Analyse non linéaire, Tome 2 (1985) no. 3, pp. 213-235. http://www.numdam.org/item/AIHPC_1985__2_3_213_0/

[1] D. Aronson and J. Serrin, Local behavior of solutions of quasilinear parabolic equations, Arch. Rat. Mech. Anal., t. 25, 1967, p. 81-122. | MR 244638 | Zbl 0154.12001

[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. | MR 430536 | Zbl 0368.35040

[3] R. Courant and K.O. Friedrichs, Supersonic Flow and Shock Waves, Wiley-Interscience New York, 1948. | MR 29615 | Zbl 0041.11302

[4] D. Hoff, Invariant regions and finite difference schemes for systems of conservation laws, Trans. Amer. Math. Soc. (to appear). | MR 784005 | Zbl 0535.35056

[5] D. Hoff and J. Smoller, Error bounds for finite difference approximations for a class of nonlinear parabolic systems, Math. Comp. (to appear). | MR 790643 | Zbl 0613.65096

[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. | MR 283426 | Zbl 0219.76080

[7] Ya. Kanel', On some systems of quasilinear parabolic equations, USSR Comp. Math. and Math. Phys., t. 6, 1966, p. 74-88. | Zbl 0157.17401

[8] Ya. Kanel', On a model system of equations of one-dimensional gas motion, Diff. Equs., t. 4, 1968, p. 374-380. | Zbl 0235.35023

[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] 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. | MR 468593 | Zbl 0393.76043

[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. | Zbl 0174.15403

[12] P. Lax, Shock waves and entropy, in Contributions to Nonlinear Functional Analysis, ed. by E. Zaratonello, Acad. Press, New York, 1971, p. 603-634. | MR 393870 | Zbl 0268.35014

[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. | MR 564670 | Zbl 0429.76040

[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. | MR 720594 | Zbl 0535.65063

[15] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer Verlag: New York, 1983. | MR 688146 | Zbl 0508.35002

[16] Ding Xiaxi and Wang Jinghua, Global solutions for a semilinear parabolic system, Acta. Math. Scientia, t. 3, 1983, p. 397-414. | Zbl 0592.65056