cauchy problem
Word Rarity
Very rare
Frequency: Zipf frequency 2.40 in modern English
29
Scrabble Score
13
Letters
2
Syllables
12
Unique Chars
Meaning
noun
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.
Example Sentences
- "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."
- "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)."
- "In this monograph we discuss the C#92;infty well-posedness of the Cauchy problem for hyperbolic systems."