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Two-dimensional Barenblatt solution with diffusivity proportional to concentration
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Mathematics
Area of mathematics
Analysis
Partial differential equation
Diffusion equation
Nonlinear diffusion equation
Created
2026-09-24
Updated
2026-10-05
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For
C
t
=
k
∇
⋅
(
C
∇
C
)
with total
mass
2
π
M
,
C
(
r
,
t
)
=
k
t
M
(
2
1
−
8
1
M
k
t
r
2
)
+
.
(1)
Its
compact support
has
radius
r
0
(
t
)
=
(
32
M
k
t
)
1/4
.
Table of contents
Linear-reaction time change for quadratic nonlinear diffusion
Two-dimensional Barenblatt solution with diffusivity proportional to concentration
Linear-reaction time change for quadratic nonlinear diffusion
0
0
0
Two-dimensional Barenblatt solution with diffusivity proportional to concentration
The substitution
C
(
x
,
t
)
=
e
a
t
G
(
x
,
τ
(
t
))
,
τ
(
t
)
=
{
(
e
a
t
−
1
)
/
a
,
t
,
a
=
0
,
a
=
0
,
(1)
reduces
C
t
=
k
∇
⋅
(
C
∇
C
)
+
a
C
to
G
τ
=
k
∇
⋅
(
G
∇
G
)
.
Ancestors
(7)
Nonlinear diffusion equation
Diffusion equation
Partial differential equation
Analysis
Area of mathematics
Mathematics
Home
Incoming links
(1)
Past exam of the mathematics course of the University of Cambridge
/
2022
/
ii
/
Paper 3
/
13C
/
Solution
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