Initial condition

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In differential equations and physics, an initial condition is any member of a set of mathematical or physical values that impose starting points for the variables in an equation that has one or more arbitrary constants.


  • In the Green-function treatment of particle motion, a unit impulse is represented by a force F(t) = δ(tt′) and is the analogue of the unit point source in spatial problems. The initial conditions play the role of boundary conditions.
  • Inflation has attracted cosmologists because of its potential to free the standard big bang model from its worst flaw, the need for special initial conditions and, in particular, the requirement of initial acausal homogeneity. Naturally one must check whether inflation itself depends critically on initial conditions. Several “no hair” theorems and perturbation calculations have indicated that inflation is stable, and that it will take place when the initial conditions are perturbed. This has led to the belief that inflation will start in any generic universe.
  • The surprising discovery of Newton’s age is just the clear separation of laws of nature on the one hand and initial conditions on the other. The former are precise beyond anything reasonable; we know virtually nothing about the latter. ,,,
    … how can we ascertain that we know all the laws of nature relevant to a set of phenomena? If we do not, we would determine unnecessarily many initial conditions in order to specify the behavior of the object.

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