最終更新日：2024/08/05
(mathematics, mathematical analysis) 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.
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Cauchy problem
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Cauchy problem
noun
(mathematics,
mathematical
analysis)
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.
意味（1）
(mathematics,
mathematical
analysis)
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.
