On the uniqueness of solutions of certain improperly posed problems.
Author:
Vincent G. Sigillito
Journal:
Proc. Amer. Math. Soc. 24 (1970), 828-831
MSC:
Primary 35.06
DOI:
https://doi.org/10.1090/S0002-9939-1970-0254403-X
MathSciNet review:
0254403
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Conditions are derived for uniqueness of solutions of some improperly posed problems for hyperbolic equations. Uniqueness results for backward parabolic problems are also included.
- 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
- 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 https://doi.org/10.1016/0022-247X%2867%2990103-5
- 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 https://doi.org/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 https://doi.org/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 https://doi.org/10.1007/BF02412914
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35.06
Retrieve articles in all journals with MSC: 35.06
Additional Information
Keywords:
Improperly posed problems,
uniqueness conditions for hyperbolic Neumann problem,
uniqueness of solutions for backward parabolic equations
Article copyright:
© Copyright 1970
American Mathematical Society