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Methods of Mathematical Physics, Vol. II: Partial Differential Equations
Courant, R. 1962 · 1962
Earlier work this paper cites.
The dimensionality of time
Dorling, J. 1970 · 1970
Earlier work this paper cites.
Partial Differential Equations
John, F. 1982 · 1982
Earlier work this paper cites.

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Contour integrals for the ultrahyperbolic wave equation. Proc. Royal Soc. London
Woodhouse, N. M. J. 1992 · 1992
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Tegmark, M. 1997 · 1997
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Duality and Strings, Space and Time
Hull, C. M. 1999 · 1999
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Then

Worldvolume Theories, Holography, Duality and Time Nucl.Phys. B575
Hull, C. M. & Khuri, R. R. 2000 · 2000
Later among the works it cites.
Survey of two-time physics
Bars, I. 2001 · 2001
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2008

On determinism and well-posedness in multiple time dimensions

Craig, Walter, Weinstein, Steven

Understand

We study the initial value problem for the wave equation and the ultrahyperbolic equation for data posed on initial surface of mixed signature (both spacelike and timelike).

Under a nonlocal constraint, we show that the Cauchy problem on codimension-one hypersurfaces has global unique solutions in the Sobolev spaces $H^{m}$, thus it is well-posed.
In contrast, we show that the initial value problem on higher codimension hypersurfaces is ill-posed, at least when specifying a finite number of derivatives of the data, due to the failure of uniqueness.
This is in contrast to a uniqueness result which Courant and Hilbert deduce from Asgeirsson's mean value theorem, for which we give an independent derivation.