@article{M2AN_1999__33_5_895_0,
author = {Aziz, A. Kadir and French, Donald A. and Jensen, Soren and Kellogg, R. Bruce},
title = {Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {895--922},
year = {1999},
publisher = {EDP Sciences},
volume = {33},
number = {5},
mrnumber = {1726715},
zbl = {0962.65082},
language = {en},
url = {https://www.numdam.org/item/M2AN_1999__33_5_895_0/}
}
TY - JOUR AU - Aziz, A. Kadir AU - French, Donald A. AU - Jensen, Soren AU - Kellogg, R. Bruce TI - Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1999 SP - 895 EP - 922 VL - 33 IS - 5 PB - EDP Sciences UR - https://www.numdam.org/item/M2AN_1999__33_5_895_0/ LA - en ID - M2AN_1999__33_5_895_0 ER -
%0 Journal Article %A Aziz, A. Kadir %A French, Donald A. %A Jensen, Soren %A Kellogg, R. Bruce %T Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem %J ESAIM: Modélisation mathématique et analyse numérique %D 1999 %P 895-922 %V 33 %N 5 %I EDP Sciences %U https://www.numdam.org/item/M2AN_1999__33_5_895_0/ %G en %F M2AN_1999__33_5_895_0
Aziz, A. Kadir; French, Donald A.; Jensen, Soren; Kellogg, R. Bruce. Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 5, pp. 895-922. https://www.numdam.org/item/M2AN_1999__33_5_895_0/
[1] and , A Galerkin method for the forward-backward heat equation. Math. Comp. 56 (1991) 35-44. | Zbl | MR
[2] and , A weighted least squares method for the backward-forward heat equation. SIAM J. Numer. Anal. 28 (1991) 156-167. | Zbl | MR
[3] and , Sur une équation d'évolution changeant de type. J. Funct. Anal 2 (1968) 352-367. | Zbl | MR
[4] , On an equation of mixed type from electron scattering. J. Math. Anal. Appl. 58 (1977) 32-45. | Zbl | MR
[5] , and , The multiple scattering of electrons. Proc. Amer. Philos. Soc. 78 (1938) 573-585. | JFM
[6] , Die Streuabsorption der Elektronenstrahlen (electron scattering). Zeit. Physik 54 (1929) 161-178. | JFM
[7] , and , Separating boundary-layer flow calculations. J. Comput. Physics (1979) 363-378. | Zbl | MR
[8] and , On the calculation of separation of bubbles. J. Fluid Mech. 133 (1983) 287-296. | Zbl
[9] , The Finite Element Methods for Elliptic Problems. North Holland (1980). | Zbl | MR
[10] , and , Large time asymptotics in contaminant transport in porous media. SIAM J. Appl. Math. 56 (1996) 965-993. | Zbl | MR
[11] and , Numerical analysis of an elliptic-parabolic partial differential equation. SIAM J. Numer. Anal. 5 (1968) 680-716. | Zbl | MR
[12] and , On a backward-forward parabolic equation and its regularization. J. Differential Equation 105 (1993) 264-295. | Zbl | MR
[13] , Continuons Galerkin Finite Element Methods for a Forward-Backward Heat Equation. Numer. Methods Partial Differential Equations 15 (1999) 257-265. | Zbl | MR
[14] , Discontinuous Galerkin Finite Element Methods for a Forward-Backward Heat Equation. Appl. Numer. Math. 27 (1998) 1-8. | Zbl | MR
[15] , Sur certaines équations aux dérivées partielles du type parabolique. Comptes Rendues 154 (1912) 1785-1788. | JFM
[16] , Sur les équations aux dérivées partielles du type parabolique, IV. J. Math. Pures Appl 10 (1914) 105-137. | JFM | Numdam
[17] , A formula for the solution of a boundary-value problem for the stationary equation of Brownian motion. Dokl. Akad. Nauk SSSR 223 (1975), also Soviet Math. Dokl. 16 (1975) 904-908. | Zbl | MR
[18] and , Half-range analysis of a counter-current separator. J. Math. Anal. Appl. 160 (1991) 358-378. | Zbl | MR
[19] , Mathematical problems of radiative equilibrium, Cambridge tracts in mathematics and mathematical physics, No. 31. Cambridge University Press (1934). | MR | JFM
[20] and , Boundary and initial boundary-value problems for separable backward-forward parabolic problems. J. Math. Phys. B 38 (1997) 4343-4353. | Zbl | MR
[21] , Über die Differentialgleichung . Math. Annal 61 (1905) 397-405. | MR | JFM
[22] and , Degenerate elliptic-parabolic equations of second order. Comm. Pure Appl. Math. 20 (1967) 797-872. | Zbl | MR
[23] , The Propagation of an Electron Beam Through the Solar Corona. Ph.D. thesis, Physics and Astronomy, University of Maryland, College Park (1986).
[24] , The spatial structure of a nonthermal electron beam: conditions for stabilization via strong turbulence. Astrophys J. 335 (1988) 425-440.
[25] , Équations différentielles opérationelles et problèmes aux limites. Springer, Berlin (1961). | Zbl | MR
[26] , Weak residual error estimates for symmetric positive Systems. Numer. Funct. Anal. Optim. 14 (1993) 607-519. | Zbl | MR
[27] , A finite difference method for symmetric positive differential equations. Math. Comp, 62 (1994) 105-118. | Zbl | MR
[28] , Galerkin and weighted Galerkin methods for the forward-backward heat equation. Numer. Math, 75 (1997) 339-56. | Zbl | MR
[29] and , Solution of a forward-baekward heat equation, preprint, Department of Mathematics, University of Nijmegen, NL (1994). | Zbl
[30] , Plasma astrophysics: non-thermal processes in diffuse magnetized plasmas. Vol. 1: The émission, absorption, and transfer of waves in plasmas. Vol. 2: Astrophysical application. Gordon and Breach, New York (1978).
[31] and , A model for laminar boundary-layer flow near a separation point, SIAM J. Appl. Math. 25 (1973) 655-670. | Zbl
[32] , Die Theorie der Integralgleichungen in Anwendung auf einige Reihenentwicklungen. Math. Annal. 66 (1910) 388-416. | JFM
[33] , Die Prandtlschen Grenzschichtdifferentialgleichungen als asymptotischer Grenzfall der Navier-Stokesschen und der Eulerschen differentialgleichungen. Arch. Rational Mech. Anal 13 (1963) 1-14. | Zbl | MR
[34] , Mathematical problems of boundary layer theory. Uspekhi Mat. Nauk 23 (1968) 3-65. | Zbl | MR
[35] and , Second order equations with nonnegative characteristic form. Plenum Press, New York-London (1973). | MR
[36] , On an initial-boundary value problem for the equation wt = wxx - xwy. Ann. Scuola Norm. Sup. Pisa, Ser. IV 2 (1975) 219-263. | Zbl | MR | Numdam
[37] , On forward-backward parabolic equations in bounded domains. Boll. Un. Mat Ita. B (5) 13 (1976) 336-354. | Zbl | MR
[38] and , The outer region of a turbulent boundary layer, Phys. Fluids A, Fluid dynamics 2 (1990) 427. | Zbl
[39] and , Solution of the thermal boundary layer equations in regions of flow reversal. SIAM J. Appl. Math. 55 (1995) 192-204. | Zbl | MR
[40] and , Numerical simulation of steady supersonic viscous flow. AIAA J. 18 (1980) 1421-1430. | Zbl | MR
[41] , Steady and unsteady boundary-layer separation. Annu. Rev. Fluid Mech 18 (1986) 197-220. | Zbl | MR
[42] and , Separation of jets or thermal boundary layers from a wall. Quart. J. Mech. Appl. Math. 30 (1977) 143-156. | Zbl | MR
[43] , Multistructural boundary layers on flat plates and related bodies. Adv. in Appl. Mech. 14 (1974) 145-239.
[44] , D'Alembert's paradox. SIAM Rev. 23 (1981) 308-343. | Zbl | MR
[45] and , Self-induced separation. Proc. Royal Soc. Ser. A 312 (1969) 181-206. | Zbl
[46] , Numerical solution of a simple Fokker-Planck equation. Appl. Numer. Math. 9 (1992) 533-540. | Zbl | MR
[47] and , Iterative methods for a forward-baekward heat equation, SIAM J. Numer. Anal. 27 (1990) 622-635. | Zbl | MR
[48] , An introduction to transport theory. John Wiley and Sons Inc., New York-London (1962). | MR





