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Cauchy problem

noun

Etymology

After French mathematician Augustin Louis Cauchy.

Definitions

  1. For a given m-order partial differential equation, the problem of finding a solution…

    For a given m-order partial differential equation, the problem of finding a solution function u on ℝⁿ that satisfies the boundary conditions that, for a smooth manifold S⊂ℝⁿ, u(x)=f_0(x) and (∂ᵏu(x))/(∂nᵏ)=f_k(x), ∀x∈S, k=1…m-1, given specified functions f_k defined on, and vector n normal to, the manifold.

    • 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.
    • In this monograph we discuss the C#92;infty well-posedness of the Cauchy problem for hyperbolic systems.

The neighborhood

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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA