Then, for some value, there exists a unique solution to the initial value problem on the interval [ t _ 0-\ varepsilon, t _ 0 + \ varepsilon ].
32.
Walter Craig and Steven Weinstein recently ( 2008 ) proved that under a nonlocal constraint, the initial value problem is well-posed for initial data given on a codimension-one hypersurface.
33.
Thus, the problem of proving the existence and uniqueness of integral curves is the same as that of finding solutions to ordinary differential equations / initial value problems and showing that they are unique.
34.
To solve the initial value problem for this equation where u ( x, 0 ) is a known function of " x ", one associates to this equation the Schr�dinger eigenvalue equation
35.
In some cases, the term " singular solution " is used to mean a solution at which there is a failure of uniqueness to the initial value problem at every point on the curve.
36.
Another problem with setting " C " equal to zero is that sometimes we want to find an antiderivative that has a given value at a given point ( as in an initial value problem ).
37.
It is also interesting to remark that although these conditions are only sufficient, there also exist necessary and sufficient conditions for the solution of an initial value problem to be unique, such as Okamura's theorem.
38.
In those cases ( called Initial value problems ), you can solve for the exact value of C that's required for the equation to hold . talk ) 12 : 04, 26 May 2007 ( UTC)
39.
One method to solve the initial value problem ( with the initial values as posed above ) is to take advantage of a special property of the wave equation in an odd number of space dimensions, namely that its solutions respect causality.
40.
Due to uniqueness of the solution to the initial value problem in question, in the particular case of zero initial conditions the Riemann solution provided by the STTD technique must coincide with the convolution of the causal Green s function and the source term.
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