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Transactions of the American Mathematical Society

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Uniqueness of solutions of the Dirichlet and Neumann problems for hyperbolic equations


Author: Eutiquio C. Young
Journal: Trans. Amer. Math. Soc. 160 (1971), 403-409
MSC: Primary 35.55
DOI: https://doi.org/10.1090/S0002-9947-1971-0282063-6
MathSciNet review: 0282063
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Abstract: Conditions for uniqueness of solutions of the Dirichlet and Neumann problems are obtained for a singular hyperbolic equation involving a real parameter.


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  • [1] D. G. Bourgin and R. Duffin, The Dirichlet problem for the vibrating string equation, Bull. Amer. Math. Soc. 45 (1939), 851-858. MR 1, 120. MR 0000729 (1:120f)
  • [2] F. John, The Dirichlet problem for a hyperbolic equation, Amer. J. Math. 63 (1941), 141-154. MR 2, 204. MR 0003346 (2:204h)
  • [3] D. W. Fox and C. Pucci, The Dirichlet problem for the wave equation, Ann. Mat. Pura Appl. (4) 46 (1958), 155-182. MR 21 #3653. MR 0104902 (21:3653)
  • [4] D. R. Dunninger and E. C. Zachmanoglou, The condition for uniqueness of solutions of the Dirichlet problem for the wave equation in coordinate rectangles, J. Math. Anal. Appl. 20 (1967), 17-21. MR 37 #1807. MR 0226217 (37:1807)
  • [5] -, The condition for uniqueness of the Dirichlet problem for hyperbolic equations in cylindrical domains, J. Math. Mech. 18 (1969), 763-766. MR 38 #4817. MR 0236522 (38:4817)
  • [6] V. G. Sigillito, On the uniqueness of solutions of certain improperly posed problems, Proc. Amer. Math. Soc. 24 (1970), 828-831. MR 40 #7612. MR 0254403 (40:7612)
  • [7] D. R. Dunninger and R. J. Weinacht, Improperly posed problems for singular equations of the fourth order, Applicable Analysis (to appear). MR 0397208 (53:1067)
  • [8] W. Walter, Über die Euler-Poisson-Darboux-Gleichung, Math. Z. 67 (1957), 361-376. MR 19, 1059. MR 0092079 (19:1059a)
  • [9] D. W. Fox, The solution and Huygen's principle for a singular Cauchy problem, J. Math. Mech. 8 (1959), 197-219. MR 21 #762. MR 0101960 (21:762)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0282063-6
Keywords: Well-posed problem, uniqueness of solutions of the Dirichlet and Neumann problems for hyperbolic equations in cylindrical domains, eigenvalues and eigenfunctions
Article copyright: © Copyright 1971 American Mathematical Society

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