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• W2045255502 abstract "Communications on Pure and Applied MathematicsVolume 31, Issue 4 p. 431-480 Article Asymptotic behavior of solutions to hyperbolic partial differential equations with zero speeds Jeffrey Rauch, Jeffrey Rauch Institute for Advanced Study and University of MichiganSearch for more papers by this author Jeffrey Rauch, Jeffrey Rauch Institute for Advanced Study and University of MichiganSearch for more papers by this author First published: July 1978 https://doi.org/10.1002/cpa.3160310404Citations: 18AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Bibliography 1 Agmon, S., Spectral properties of Schrödinger operators and scattering theory, Ann. Scuola Norm. Sup. Pisa, 1975, pp. 151– 218. 2 Agmon, S., and Hörmander, L., Asymptotic properties of differential equations with simple characteristics, J. d'Analyse Mathématique, XXX, 1976, pp. 1– 39. 3 Andersson, K., and Melrose, R., Propagation of singularities along gliding rays, Seminaire Goulaouic-Schwartz, 1976–1977. 4 Atiyah, M., Bott, R., and Gårding, L., Lacunas for hyperbolic differential operators with constant coefficients I, Acta Math. 124, 1970, pp. 109– 189. 5 Courant, R., Methods of Mathematical Physics, Vol. II, Interscience, New York, 1966. 6 Dolph, C., McLeod, J., and Thoe, D., The analytic continuation of the resolvent kernel and scattering operator associated with the Schrödinger operator, J. Math. Anal. Appl. 16, 1966, pp. 311– 332. 7 Eskin, G., A parametrix for the mixed problems for strictly hyperbolic equations of an arbitrary order, Comm. Partial Diff. Equa., 1976, pp. 521– 560. 8 Hunziker, W., The Schrödinger eigenvalue problem for N-particle systems, Acta Physica Austrica, to appear. 9 Iwasaki, N., Local decay of solutions for symmetric hyperbolic systems with dissipative and coercive boundary conditions in exterior domains, Publ. RIMS Kyoto Univ. 5, 1969, pp. 193– 218. 10 Lax, P., Lectures on Hyperbolic Partial Differential Equations, Lecture Notes, Stanford University, 1963. 11 Lax, P., and Phillips, R., Scattering theory, Rocky Mtn. J. of Math. 1, 1971, pp. 173– 223. 12 Lax, P., and Phillips, R., Scattering theory for dissipative hyperbolic systems, J. Funct. Anal. 14, 1973, pp. 172– 235. 13 Ludwig, D., Exact and asymptotic solutions of the Cauchy problem. Comm. Pure Appl. Math. 13, 1960, pp. 473– 508. 14 MacCamy, R., Low frequency acoustic oscillations, Quart. Appl. Math. 28, 1965, pp. 247– 255. 15 Majda, A., and Osher, S., Initial boundary value problems for hyperbolic equations with uniformly characteristic boundary, Comm. Pure Appl. Math. 28, 1975, pp. 607– 675. 16 Melrose, R., Microlocal parametrices for diffractive boundary value problems, Duke Math. J. 42, 1975, pp. 605– 635. 17 Morawetz, C., Ralston, J., and Strauss, W., Decay of solutions of the wave equation outside nontrapping obstacles, Comm. Pure Appl. Math., 30, 1977, pp. 447– 508. 18 Phillips, R., and Sarason, L., Energy decay for the neutrino equation in the exterior of a torus, Arch. Rat. Mech. Anal. 41, 1971, pp. 1– 17. 19 Ralston, J., Local decay of solution of conservative first order hyperbolic systems in odd-dimensional space, Trans. A.M.S., 194, 1974, pp. 27– 51. 20 Rauch, J., and Massey, F., Differentiability of solutions to hyperbolic initial-boundary value problems, Trans. A.M.S. 189, 1974, pp. 303– 318. 21 Reed, M., and Simon, B., Methods of Modern Mathematical Physics, Vol. I Functional Analysis, Academic Press, New York, 1972. 22 Rudin, W., Functional Analysis, McGraw-Hill, New York, 1973. 23 Schulenberger, J., and Wilcox, C., Eigenfunction expansions and scattering theory for wave propagation problems of classical physics, Archiv. Rat. Mech. Anal. 46, 1972, pp. 280– 320. 24 Taylor, M., Pseudo-Differential Operators, Lecture Notes in Math. 414, Springer-Verlag, New York, 1974. 25 Taylor, M., Grazing rays and reflection of singularities to wave equations, Comm. Pure Appl. Math. 29, 1976, pp. 1– 47 and 463–481. 26 Vainberg, B., The analytic properties of the resolvent for a class of bundles of operators, Mat. Sb. 77, 1968, pp. 259– 296. 27 Vainberg, B., On exterior elliptic problems with polynomial dependence on the spectral parameter and the asymptotic behavior for large time values of the solution of non-stationary problems, Mat. Sb. 92, 1973, pp. 224– 241. 28 Vainberg, B., On the short wave asymptotic behavior of solutions of stationary problems and the asymptotic behavior as t→ ∞ of solutions of nonstationary problems, Russian Math. Surveys 30: 2, 1975, pp. 1– 58. 29 Wilcox, C., Wave operators and asymptotic solutions of wave propagation problems of classical physics, Arch. Rat. Mech. Anal. 22, 1966, pp. 37– 78. Citing Literature Volume31, Issue4July 1978Pages 431-480 ReferencesRelatedInformation" @default.
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