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

Young, Eutiquio C.

doi:10.1090/S0002-9947-1971-0282063-6

Uniqueness of solutions of the Dirichlet and Neumann problems for hyperbolic equations
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by Eutiquio C. Young PDF

Trans. Amer. Math. Soc. 160 (1971), 403-409 Request permission

Abstract:

Conditions for uniqueness of solutions of the Dirichlet and Neumann problems are obtained for a singular hyperbolic equation involving a real parameter.

References

D. G. Bourgin and R. Duffin, The Dirichlet problem for the virbrating string equation, Bull. Amer. Math. Soc. 45 (1939), 851–858. MR 729, DOI 10.1090/S0002-9904-1939-07103-6
Fritz John, The Dirichlet problem for a hyperbolic equation, Amer. J. Math. 63 (1941), 141–154. MR 3346, DOI 10.2307/2371285
David W. Fox and Carlo Pucci, The Dirichlet problem for the wave equation, Ann. Mat. Pura Appl. (4) 46 (1958), 155–182. MR 104902, DOI 10.1007/BF02412914
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 226217, DOI 10.1016/0022-247X(67)90103-5
D. R. Dunninger and E. C. Zachmanoglou, The condition for uniqueness of the Dirichlet problem for hyperbolic equations in cylindrical domains, J. Math. Mech. 18 (1969), 763–766. MR 0236522
Vincent G. Sigillito, On the uniqueness of solutions of certain improperly posed problems, Proc. Amer. Math. Soc. 24 (1970), 828–831. MR 254403, DOI 10.1090/S0002-9939-1970-0254403-X
D. R. Dunninger and R. J. Weinacht, Improperly posed problems for singular equations of the fourth order, Applicable Anal. 4 (1974/75), no. 4, 331–341. MR 397208, DOI 10.1080/00036817508839100
Wolfgang Walter, Über die Euler-Poisson-Darboux-Gleichung, Math. Z. 67 (1957), 361–376 (German). MR 92079, DOI 10.1007/BF01258869
David W. Fox, The solution and Huygens’ principle for a singular Cauchy problem, J. Math. Mech. 8 (1959), 197–219. MR 0101960, DOI 10.1512/iumj.1959.8.58015