Bardos, Claude; Rauch, Jeffrey Maximal positive boundary value problems as limits of singular perturbation problems. (English) Zbl 0485.35010 Trans. Am. Math. Soc. 270, 377-408 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 22 Documents MSC: 35B25 Singular perturbations in context of PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:linear singular perturbation problems; maximal positive boundary value problems; boundary layers PDFBibTeX XMLCite \textit{C. Bardos} and \textit{J. Rauch}, Trans. Am. Math. Soc. 270, 377--408 (1982; Zbl 0485.35010) Full Text: DOI References: [1] C. Bardos, D. Brézis, and H. Brezis, Perturbations singulières et prolongements maximaux d’opérateurs positifs, Arch. Rational Mech. Anal. 53 (1973/74), 69 – 100 (French). · Zbl 0281.47028 · doi:10.1007/BF00735701 [2] K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math. 7 (1954), 345 – 392. · Zbl 0059.08902 · doi:10.1002/cpa.3160070206 [3] K. O. Friedrichs, Symmetric positive linear differential equations, Comm. Pure Appl. Math. 11 (1958), 333 – 418. · Zbl 0083.31802 · doi:10.1002/cpa.3160110306 [4] -, Well-posed problems of mathematical physics, mimeographed lecture notes, New York Univ. [5] L. Hörmander, Linear partial differential operators, 2nd rev. printing, Springer-Verlag, Berlin, 1964. [6] Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. · Zbl 0148.12601 [7] Tosio Kato, Singular perturbation and semigroup theory, Turbulence and Navier-Stokes equations (Proc. Conf., Univ. Paris-Sud, Orsay, 1975) Springer, Berlin, 1976, pp. 104 – 112. Lecture Notes in Math., Vol. 565. [8] P. D. Lax and R. S. Phillips, Local boundary conditions for dissipative symmetric linear differential operators, Comm. Pure Appl. Math. 13 (1960), 427 – 455. · Zbl 0094.07502 · doi:10.1002/cpa.3160130307 [9] J.-L. Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lecture Notes in Mathematics, Vol. 323, Springer-Verlag, Berlin-New York, 1973 (French). · Zbl 0268.49001 [10] Jeffrey Rauch and Michael Taylor, Potential and scattering theory on wildly perturbed domains, J. Funct. Anal. 18 (1975), 27 – 59. · Zbl 0293.35056 · doi:10.1016/0022-1236(75)90028-2 [11] Leonard Sarason, On weak and strong solutions of boundary value problems, Comm. Pure Appl. Math. 15 (1962), 237 – 288. · Zbl 0139.28302 · doi:10.1002/cpa.3160150301 [12] Leonard Sarason, Differentiable solutions of symmetrizable and singular symmetric first order systems, Arch. Rational Mech. Anal. 26 (1967), 357 – 384. · Zbl 0162.40901 · doi:10.1007/BF00281640 [13] David S. Tartakoff, Regularity of solutions to boundary value problems for first order systems, Indiana Univ. Math. J. 21 (1971/72), 1113 – 1129. · Zbl 0235.35019 · doi:10.1512/iumj.1972.21.21089 [14] M. I. Višik and L. A. Lyusternik, Regular degeneration and boundary layer for linear differential equations with small parameter, Uspehi Mat. Nauk (N.S.) 12 (1957), no. 5(77), 3 – 122 (Russian). · Zbl 0087.29602 [15] M. I. Višik and L. A. Ljusternik, The asymptotic behaviour of solutions of linear differential equations with large or quickly changing coefficients and boundary conditions, Russian Math. Surveys 15 (1960), no. 4, 23 – 91. · Zbl 0098.06501 · doi:10.1070/RM1960v015n04ABEH004096 [16] Calvin H. Wilcox, Wave operators and asymptotic solutions of wave propagation problems of classical physics, Arch. Rational Mech. Anal. 22 (1966), 37 – 78. · Zbl 0159.14302 · doi:10.1007/BF00281244 [17] J. Rauch, Boundary value problems as limits of problems in all space, Séminaire Goulaouic-Schwartz (1978/1979), École Polytech., Palaiseau, 1979, pp. Exp. No. 3, 17. · Zbl 0435.35052 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.