An approximate layering method for multi-dimensional nonlinear parabolic systems of a certain type
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 6 (1979) no. 2, pp. 193-283.
@article{ASNSP_1979_4_6_2_193_0,
     author = {Douglis, Avron},
     title = {An approximate layering method for multi-dimensional nonlinear parabolic systems of a certain type},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {193--283},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 6},
     number = {2},
     year = {1979},
     zbl = {0407.35049},
     mrnumber = {541449},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1979_4_6_2_193_0/}
}
TY  - JOUR
AU  - Douglis, Avron
TI  - An approximate layering method for multi-dimensional nonlinear parabolic systems of a certain type
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1979
DA  - 1979///
SP  - 193
EP  - 283
VL  - Ser. 4, 6
IS  - 2
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1979_4_6_2_193_0/
UR  - https://zbmath.org/?q=an%3A0407.35049
UR  - https://www.ams.org/mathscinet-getitem?mr=541449
LA  - en
ID  - ASNSP_1979_4_6_2_193_0
ER  - 
%0 Journal Article
%A Douglis, Avron
%T An approximate layering method for multi-dimensional nonlinear parabolic systems of a certain type
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1979
%P 193-283
%V Ser. 4, 6
%N 2
%I Scuola normale superiore
%G en
%F ASNSP_1979_4_6_2_193_0
Douglis, Avron. An approximate layering method for multi-dimensional nonlinear parabolic systems of a certain type. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 6 (1979) no. 2, pp. 193-283. http://www.numdam.org/item/ASNSP_1979_4_6_2_193_0/

[1] A.J. Chorin, Numerical study of slightly viscous flow, J. Fluid Mech., 57 (1973), pp. 785-796. | MR

[2] A.J. Chorin - T.J.R. Hughes - M.F. Mccracken - J.E. Marsden, Product formulas and numerical algorithms (1977), presumably to appear. | MR | Zbl

[3] H. Cramér, Mathematical methods of statistics, Princeton Univ. Press, Princeton, N. J. (1946). | MR | Zbl

[4] A. Douglis, Layering methods for nonlinear partial differential equations of first order, Ann. Inst. Fourier Univ. Grenoble, 22 (1972), pp. 141-227. | Numdam | MR | Zbl

[5] A. Douglis, Lectures on discontinuous solutions of first order nonlinear partial differential equations, North British Symposium on Partial Differential Equations and their Applications. School of Mathematics, University of Newcastleon-Tyne (1972) (multilithed).

[6] A. Douglis, Layering methods for parabolic systems, Preliminary report. Notices Amer. Math. Soc., 22 (1975), p. A152.

[7] S.D. Eidel'Man, Parabolic systems, North Holland Pub. Co., Amsterdam, 1969. | MR | Zbl

[8] A. Friedman, Remarks on nonlinear parabolic equations, Proc. Symp. Appl. Math., 17 (1965), pp. 3-23. | MR | Zbl

[9] H. Fujita, On some non-existence and non-uniqueness theorems for nonlinear parabolic equations, Proc. Symp. Pure Math., 18 (Part 1) (1970), pp. 105-113. | MR | Zbl

[10] R.T. Glassey, Blow-up theorems for nonlinear wave equations, Math. Z., 132 (1973), pp. 183-203. | MR | Zbl

[11] A. Jeffrey, Stability of parabolic systems, Indiana Univ. Math. J., 22 (1973), pp. 1109-1135. | MR | Zbl

[12] H. Kawarada, On the solutions of initial-boundary problems for ut = uxx + + 1/(1 - u), Publ. Res. Inst. Math. Sci., 10, no. 3 (1974-1975), pp. 729-736. | MR | Zbl

[13] N.N. Kuznetsov, Weak solution of the Cauchy problem for a multi-dimensional quasilinear equation, Mat. Zametki, 2 (1967), pp. 401-410; transl.: Math. Notes, (1967), pp. 733-739. | MR | Zbl

[14] N.N. Kuznetsov, Application of the smoothing method to some systems of hyperbolic quasilinear equations, Ž. Vyčisl. Mat. i Mat. Fiz.,13 (1973), pp. 92-102; transl.: USSR Comput. Math. and Math. Phys., 13 (1974), pp. 115-129. | MR | Zbl

[15] O.A. Ladyzhenskaya - V.A. Solonnikov - N.N. Ural'Ceva, Linear and quasilinear equations of parabolic type, Translations of mathematical monographs, vol. 23, A.M.S., Providence, 1968. | Zbl

[16] H.A. Levine, Some nonexistence and instability theorems for solutions of formally parabolic equations of the form Put = Au + F(u), Arch. Rational Mech. Anal., 51 (1973), pp. 371-386. | MR | Zbl

[17] H.A. Levine, Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics : the method of unbounded Fourier coefficients, Math. Ann., 214 (1975), pp. 205-220. | MR | Zbl

[18] H.A. Levine - L.E. Payne, On the nonexistence of global solutions to some abstract Cauchy problems of standard and nonstandard types, Rend. Mat., (6) 8, no. 2 (1975), pp. 413-428. | MR | Zbl

[19] J. Marsden, On product formulas for nonlinear semigroups, J. Functional Analysis, 13 (1973), pp. 51-72. | MR | Zbl

[20] J. Marsden, A formula for the solution of the Navier-Stokes equations based on a method of Chorin, Bull. Amer. Math. Soc., 80 (1974), pp. 154-158. | MR | Zbl

[21] A. Pazy, Semi-groups of linear operators and applications to partial differential equations, Lecture Notes no. 10, Math. Dept., Univ. of Maryland, College Park, Md., 1974. | MR

[22] V.V. Petrov, Sums of independent random variables, Springer, New York, 1975. | MR | Zbl

[23] I.J. Schoenberg, On smoothing operations and their generating functions, Bull. Amer. Math. Soc., 59 (1953), pp. 199-230. | MR | Zbl

[24] F. Treves, Approximate solution to Cauchy problems, J. Differential Equations, 11 (1972), pp. 349-363. | MR | Zbl

[25] M. Tsutsumi,, On solutions of semilinear differential equations in a Hilbert space, Math. Japon., 17 (1972), pp. 173-193. | MR | Zbl

[26] M. Tsutsumi, Existence and nonexistence of global solutions of the first boundary value problem for a certain quasi linear parabolic equation, Funkcial. Ekvac., 17 (1974), pp. 13-24. | MR | Zbl

[27] M.I. Visik, Boundary-value problems for quasilinear parabolic systems of equations and Cauchy's problem for hyperbolic equations, Dokl. Akad. Nauk SSSR, 140 (1961), pp. 998-1001; transl.: Soviet Math. Dokl., 2 (1961), pp. 1292-1295. | MR | Zbl

[28] W. Von Wahl, Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetigen Funktionen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, (1972), no. 11, pp. 231-258. | MR | Zbl

[29] W. Von Wahl, Einige Bemerkungen zu meiner Arbeit « Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetigen Funktionen, Manuscripta Math., 11 (1974), pp. 199-201. | MR | Zbl

[30] W. Von Wahl, Semilineare parabolische Differentiagleichungen mit starker Nichtlinearität, Manuscripta Math., 16, no. 4 (1975), pp. 395-406. | MR | Zbl

[31] T.D. Wentzell, An a priori estimate for the solution of some quasi-linear parabolic systems, Vestnik Moskow. Univ. Ser. I Mat. Meh. 29, no. 1 (1974), pp. 37-44 (transl. in Moscow University Mathematica Bulletin, 29, no. 1 (1974), pp. 28-34). | MR | Zbl