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Initial-boundary value problems for hyperbolic systems in regions with corners. II. (English) Zbl 0256.35051


MSC:

35L50 Initial-boundary value problems for first-order hyperbolic systems
35L30 Initial value problems for higher-order hyperbolic equations
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[1] T. Elvius and A. Sundström, Computationally efficient schemes and boundary conditions for afine mesh barotropic model based on shallow water equations, Tellus, 25 (1973), 132-156.
[2] V. A. Kondrat\(^{\prime}\)ev, Boundary-value problems for elliptic equations in conical regions, Dokl. Akad. Nauk SSSR 153 (1963), 27 – 29 (Russian).
[3] Heinz-Otto Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970), 277 – 298. · Zbl 0188.41102 · doi:10.1002/cpa.3160230304
[4] I. A. K. Kupka and S. J. Osher, On the wave equation in a multi-dimensional corner, Comm. Pure Appl. Math. 24 (1971), 381 – 393. · Zbl 0216.12802 · doi:10.1002/cpa.3160240304
[5] Stanley Osher, Initial-boundary value problems for hyperbolic systems in regions with corners. I, Trans. Amer. Math. Soc. 176 (1973), 141 – 164. · Zbl 0253.35059
[6] -, A symmetrizer for certain hyperbolic mixed problems with singular coefficients, Indiana J. Math. 22 (1973), 667-671. · Zbl 0235.35055
[7] Stanley Osher, An ill posed problem for a hyperbolic equation near a corner, Bull. Amer. Math. Soc. 79 (1973), 1043 – 1044. · Zbl 0268.35064
[8] -, On a generalized reflection principle and a transmission problem for a hyperbolic equation, Indiana J. Math. 79 (1973), 1043-1044. · Zbl 0268.35064
[9] James V. Ralston, Note on a paper of Kreiss, Comm. Pure Appl. Math. 24 (1971), no. 6, 759 – 762. · doi:10.1002/cpa.3160240603
[10] Reiko Sakamoto, Mixed problems for hyperbolic equations. I. Energy inequalities, J. Math. Kyoto Univ. 10 (1970), 349 – 373. Reiko Sakamoto, Mixed problems for hyperbolic equations. II. Existence theorems with zero initial datas and energy inequalities with initial datas, J. Math. Kyoto Univ. 10 (1970), 403 – 417. · Zbl 0206.40101
[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
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