×

Perturbations singulières et prolongements maximaux d’opérateurs positifs. (French) Zbl 0281.47028


MSC:

47F05 General theory of partial differential operators
35B25 Singular perturbations in context of PDEs
47A20 Dilations, extensions, compressions of linear operators
47A55 Perturbation theory of linear operators
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Agranovic, M. S., Positive boundary problems. Dokl. Akad. Nauk. SSSR.167, 1215-1218 (1966). Traduit dans Soviet Math.7, 539-542 (1966)
[2] Bardos, C., Sur un théorème de perturbation. C.R. Acad. Sc. (A)265, 169-172 (1967) · Zbl 0166.12502
[3] Bardos, C., Problèmes aux limites pour les équations du premier ordre. Ann. Sci. Ec. Norm. Sup.3, 185-233 (1970) · Zbl 0202.36903
[4] Bourbaki, N., Espaces Vectoriels Topologiques. Tome 2. Paris: Hermann · Zbl 0042.35302
[5] Brézis, D., A paraitre
[6] Brézis, H., Monotonicity methods in Hilbert spaces and some applications to non-linear partial differential equations. Contributions to Non Linear Functional Analysis. E.Zarantonello, ed. Acad. Press (1971), 101-156
[7] Brézis, H., Problèmes unilatéraux. J. Math. Pures Appl.51, 1-164 (1972)
[8] Chazarain, J., Problèmes de Cauchy abstraits. J. Funct. Anal.7, 386-446 (1971) · Zbl 0211.12902
[9] Faris, W. G., The product formula for semi-groups. Pacific J. Math.21, 47-70 (1967) · Zbl 0158.14802
[10] Friedrichs, K., Symmetric positive systems of differential equations. Comm. Pure App. Math.7, 345-392 (1954) · Zbl 0059.08902
[11] Huet, D., Phénomène de perturbation singulière. Ann. Inst. Fourier10, 61-151 (1960) · Zbl 0128.32904
[12] Ikawa, M., Mixed problems for hyperbolic systems. Pub. Res. Inst. Mat. Sci. Kyoto U.7, 427-454 (1971) · Zbl 0231.35051
[13] Kato, T., Perturbation Theory For Linear Operators. Berlin-Heidelberg-New York: Springer 1966 · Zbl 0148.12601
[14] Lax, P., & R. S.Phillips, Local boundary conditions. Comm. Pure. App. Math.13, 427-455 (1960) · Zbl 0094.07502
[15] Levinson, N., The first boundary value problem for??u+A(x,y)u x +B(x,y)u y +C(x,y)u=D(x,y) for small ?. Ann. Math.5, 428-445 (1950) · Zbl 0036.06801
[16] Lions, J. L., Singular perturbations and singular layers in variational inequalities. Contributions to Non-Linear Functional Analysis. E. Zarantonello, ed. Acad. Press 523-564 (1971)
[17] Oleinik, O., Linear equations of second order. Mat. Sb.69, 111-140 (1966), Amer Math. Soc. Transl. Series 2,65, 167-200 (1967)
[18] Petrovski, I. G., Über das Cauchysche Problem. Mat. Sb.2, 815-868 (1937) · Zbl 0018.40503
[19] Phillips, R. S., & L.Sarason, Singular symmetric positive first order differential operators. J. Math. Mech.15, 235-272 (1966) · Zbl 0141.28701
[20] Schmidt, G., Spectral and scattering theory for Maxwell’s equations. Arch. Rat. Mech. Anal.28, 284-322 (1968) · Zbl 0155.43502
[21] Sivasinskii, S. V., The introduction of ?viscosity? into first order linear symmetric systems. Vestnik Leningrad Univ.25, 54-57 (1970)
[22] Trotter, H. F., Approximation of semi-groups. Pacific J. Math.8, 887-919 (1958) · Zbl 0099.10302
[23] Trotter, H. F., On the product of semi-groups. Proc. Amer. Soc.10, 545-551 (1959) · Zbl 0099.10401
[24] Visik, M. I., & L. A.Lyusternik, Regular degeneration and boundary layer for linear differential equations with small parameter. Uspekhi Mat Nauk.12, 3-122 (1957), Amer. Math. Soc. Trans. (20)20, 239-364 (1962) · Zbl 0087.29602
[25] Yosida, K., Functional Analysis. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0217.16001
[26] Ilin, A. M., Sur le comportement asymptotique de la solution d’un problème aux limites. Mat. Zametki.8, 273-284 (1970)
[27] Ilin, A. M., Sur le comportement de la solution d’un problème aux limites pour t??. Mat. Sb.81, 530-553 (1972)
[28] Phillips, R. S., Semi Groups of Contraction, C.I.M.E. Equazioni differenziali astratte. Roma: Edizioni Cremonese 1963
[29] Smoller, J. A., & M. E.Taylor, Wave front sets and the viscosity method, Bull. Am. Math. Soc.79, 431-436 (1973) · Zbl 0256.35010
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.