Phrase guide

Cauchy problem

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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1

noun

Meaning 1

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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematical-analysis, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

After French mathematician Augustin Louis Cauchy.

Across languages

Translations

3 source translations are retained for this English entry.

  • Bulgarian: задача на Коши (zadača na Koši) — class of problem involving simultaneous PDEs
  • Italian: problema di Cauchy — class of problem involving simultaneous PDEs
  • Polish: zagadnienie Cauchy'ego — class of problem involving simultaneous PDEs