×

zbMATH — the first resource for mathematics

Uniqueness of solution of an inverse source problem for ultrahyperbolic equations. (English) Zbl 1446.45010

MSC:
45K05 Integro-partial differential equations
35L82 Pseudohyperbolic equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Amirov A Kh 2001 Integral Geometry and Inverse Problems for Kinetic Equations (Utrecht: VSP) · Zbl 1040.53001
[2] Amirov A Kh 2001 One class of inverse problems for an ultrahyperbolic equation Doklady Math.64 22-4 · Zbl 1048.35126
[3] Amirov A Kh and Yamamoto M 2005 Unique continuation and an inverse problem for hyperbolic equations across a general hypersurface J. Phys.: Conf. Ser.12 1-12
[4] Bars I 2001 Survey of two-time physics Class. Quantum Grav.18 3113-30 · Zbl 0990.83010
[5] Bellassoued M and Yamamoto M 2017 Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems (Tokyo: Springer) · Zbl 1412.35002
[6] Bukhgeim A L and Klibanov M V 1981 Global uniqueness of a class of multidimensional inverse problems Sov. Math.—Dokl.24 244-7 · Zbl 0497.35082
[7] Burskii V P and Kirichenko E V 2008 Unique solvability of the Dirichlet problem for an ultrahyperbolic equation in a ball Differ. Equ.44 486-98 · Zbl 1172.35457
[8] Courant R and Hilbert D 1962 Methods of Mathematical Physics(Partial Differential Equations. Interscience vol II) (New York: Interscience)
[9] Craig W and Weinstein S 2009 On determinism and well-posedness in multiple time dimensions Proc. R. Soc. A 465 3023-46 · Zbl 1181.35140
[10] Diaz J B and Young E C 1971 Uniqueness of solutions of certain boundary value problems for ultrahyperbolic equations Proc. Am. Math. Soc.29 569-74 · Zbl 0237.35017
[11] Gölgeleyen F and Yamamoto M 2014 Stability of inverse problems for ultrahyperbolic equations Chin. Ann. Math. B 35 527-56 · Zbl 1335.35295
[12] Hörmander L 1963 Linear Partial Differential Operators (Berlin: Springer) · Zbl 0171.06802
[13] Hörmander L 2001 Asgeirsson’s mean value theorem and related identities J. Funct. Anal.184 377-401 · Zbl 1019.35022
[14] Klibanov M V and Timonov A 2004 Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (Utrecht: VSP) · Zbl 1069.65106
[15] Kostomarov D P 2002 A Cauchy problem for an ultrahyperbolic equation Differ. Equ.38 1155-61 · Zbl 1029.35069
[16] Lavrent’ev M M, Romanov V G and Shishatskiĭ S P 1986 Ill-Posed Problems of Mathematical Physics and Analysis (Providence, RI: American Mathematical Society)
[17] Murray A C 1977 Asymptotic behavior and uniqueness for an ultrahyperbolic equation with variable coefficients J. Differ. Equ.23 200-15 · Zbl 0304.35009
[18] Owens O G 1947 Uniqueness of solutions of ultrahyperbolic partial differential equations Am. J. Math.69 184-8 · Zbl 0034.36102
[19] Romanov V G 2006 Estimate for the solution to the Cauchy problem for an ultrahyperbolic inequality Dokl. Math.74 751-4 · Zbl 1146.35099
[20] Sparling G A J 2007 Germ of a synthesis: space-time is spinorial, extra dimensions are time-like, Proc. R. Soc. A 463 1665-79 · Zbl 1134.81380
[21] Tegmark M 1997 On the dimensionality of space-time Class. Quantum Grav.14 L69-75 · Zbl 0879.53071
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.