@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},
year = {1979},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 6},
number = {2},
mrnumber = {541449},
zbl = {0407.35049},
language = {en},
url = {https://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 SP - 193 EP - 283 VL - 6 IS - 2 PB - Scuola normale superiore UR - https://www.numdam.org/item/ASNSP_1979_4_6_2_193_0/ 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 6 %N 2 %I Scuola normale superiore %U https://www.numdam.org/item/ASNSP_1979_4_6_2_193_0/ %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, Série 4, Tome 6 (1979) no. 2, pp. 193-283. https://www.numdam.org/item/ASNSP_1979_4_6_2_193_0/
[1] , Numerical study of slightly viscous flow, J. Fluid Mech., 57 (1973), pp. 785-796. | MR
[2] - - - , Product formulas and numerical algorithms (1977), presumably to appear. | Zbl | MR
[3] , Mathematical methods of statistics, Princeton Univ. Press, Princeton, N. J. (1946). | Zbl | MR
[4] , Layering methods for nonlinear partial differential equations of first order, Ann. Inst. Fourier Univ. Grenoble, 22 (1972), pp. 141-227. | Zbl | MR | Numdam
[5] , 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] , Layering methods for parabolic systems, Preliminary report. Notices Amer. Math. Soc., 22 (1975), p. A152.
[7] , Parabolic systems, North Holland Pub. Co., Amsterdam, 1969. | Zbl | MR
[8] , Remarks on nonlinear parabolic equations, Proc. Symp. Appl. Math., 17 (1965), pp. 3-23. | Zbl | MR
[9] , On some non-existence and non-uniqueness theorems for nonlinear parabolic equations, Proc. Symp. Pure Math., 18 (Part 1) (1970), pp. 105-113. | Zbl | MR
[10] , Blow-up theorems for nonlinear wave equations, Math. Z., 132 (1973), pp. 183-203. | Zbl | MR
[11] , Stability of parabolic systems, Indiana Univ. Math. J., 22 (1973), pp. 1109-1135. | Zbl | MR
[12] , 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. | Zbl | MR
[13] , 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. | Zbl | MR
[14] , 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. | Zbl | MR
[15] - - , Linear and quasilinear equations of parabolic type, Translations of mathematical monographs, vol. 23, A.M.S., Providence, 1968. | Zbl
[16] , 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. | Zbl | MR
[17] , 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. | Zbl | MR
[18] - , 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. | Zbl | MR
[19] , On product formulas for nonlinear semigroups, J. Functional Analysis, 13 (1973), pp. 51-72. | Zbl | MR
[20] , 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. | Zbl | MR
[21] , 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] , Sums of independent random variables, Springer, New York, 1975. | Zbl | MR
[23] , On smoothing operations and their generating functions, Bull. Amer. Math. Soc., 59 (1953), pp. 199-230. | Zbl | MR
[24] , Approximate solution to Cauchy problems, J. Differential Equations, 11 (1972), pp. 349-363. | Zbl | MR
[25] ,, On solutions of semilinear differential equations in a Hilbert space, Math. Japon., 17 (1972), pp. 173-193. | Zbl | MR
[26] , 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. | Zbl | MR
[27] , 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. | Zbl | MR
[28] , 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. | Zbl | MR
[29] , Einige Bemerkungen zu meiner Arbeit « Gebrochene Potenzen eines elliptischen Operators und parabolische Differentialgleichungen in Räumen hölderstetigen Funktionen, Manuscripta Math., 11 (1974), pp. 199-201. | Zbl | MR
[30] , Semilineare parabolische Differentiagleichungen mit starker Nichtlinearität, Manuscripta Math., 16, no. 4 (1975), pp. 395-406. | Zbl | MR
[31] , 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). | Zbl | MR






