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Wave fronts for solutions of boundary-value problems for a class of symmetric hyperbolic systems. (English) Zbl 0458.35062


MSC:

35L67 Shocks and singularities for hyperbolic equations
35L50 Initial-boundary value problems for first-order hyperbolic systems
58J47 Propagation of singularities; initial value problems on manifolds

Citations:

Zbl 0447.35055
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Full Text: DOI

References:

[1] V. Ya. Ivrii, ?Wave fronts of solutions of symmetric pseudodifferential systems,? Sib. Mat. Zh.,20, No. 3, 557-578 (1979).
[2] V. Ya. Ivrii, ?Wave fronts of solutions of boundary-value problems for symmetric hyperbolic systems. I. The main theorem,? Sib. Mat. Zh.,20, No. 4, 741-751 (1979).
[3] V. Ya. Ivrii, ?Wave fronts of solutions of boundary-value problems for symmetric hyperbolic systems. II. Systems with characteristics of constant multiplicity,? Sib. Mat. Zh.,20, No. 5, 1022-1038 (1979).
[4] V. Ya. Ivrii, ?Wave fronts of solutions of boundary-value problems for symmetric hyperbolic systems. III. Systems with characteristics of variable multiplicity,? Sib. Mat. Zh.,20, No. 1, 74-81 (1979).
[5] V. Ya. Ivrii, ?Propagation of wave fronts of solutions of the wave equation along the boundary of a domain,? Usp. Mat. Nauk,32, No. 5, 185-186, (1977).
[6] K. G. Andersson and R. B. Melrose, ?The propagation of singularities along gliding rays,? Invent. Math.,41, No. 2, 197-232 (1977). · Zbl 0373.35053
[7] G. Eskin, ?A parametric for interior mixed problems for strictly hyperbolic equations,? J. Anal. Math.,32, No. 1, 17-62 (1977). · Zbl 0375.35037
[8] R. B. Melrose, ?Microlocal parametrices for diffractive boundary value problems,? Duke Math. J.,42, No. 6, 605-635 (1975). · Zbl 0368.35055
[9] M. E. Taylor, ?Grazing rays and reflection of singularities of solutions to the wave equation,? Commun. Pure Appl. Math.,29, No. 1, 1-38 (1976). · Zbl 0318.35009
[10] G. Eskin, ?A parametrix for mixed problems for the strictly hyperbolic equations of an arbitrary order,? Commun. Part. Diff. Eqs.1, No. 6, 521-560 (1976). · Zbl 0355.35053
[11] R. B. Melrose and J. Sjöstrand, ?Singularities of boundary-value problems. I,? Commun. Pure Appl. Math.,31, No. 5, 593-617 (1978). · Zbl 0378.35014
[12] R. B. Melrose and J. Sjöstrand, ?Singularities of boundary-value problems. II,? Preprint, Princeton (1978). · Zbl 0368.35020
[13] V. Ya. Ivrii, ?Propagation of singularities of the solution of the wave equation near the boundary,? Dokl. Akad. Nauk SSSR, 239, No. 4, 772-774 (1978).
[14] C. S. Morawetz, J. V. Ralston, and W. A. Strauss, ?Decay of solutions of the wave equation outside nontrapping obstacles,? Commun. Pure Appl. Math.,30, No. 5, 447-508 (1977). · Zbl 0372.35008
[15] B. Melgrange, Ideals of Differentiable Functions, Oxford Univ. Press (1966).
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