In this chapter we formulate and in many cases prove results on uniqueness and stability of solutions of the Cauchy problem for general partial differential equations.
Source: wiktionary
Cauchy problem
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To emphasize the similarity between the characteristic method and the probabilistic approach we recall that the method of characteristics allows [one] to reduce the Cauchy problem for a first order PDE to a Cauchy problem for an ODE while the probabilistic approach allows [one] to reduce the Cauchy problem for a second order PDE to a Cauchy problem for an SDE (stochastic differential equation).
Source: wiktionary
In this monograph we discuss the C#92;infty well-posedness of the Cauchy problem for hyperbolic systems.
Source: wiktionary