Numerical Modelling of Nonlinear Diffusion Phenomena on a Sphere - Simulation and Modeling Methodologies, Technologies and Application - page 60

56.5255

56.5254

56.5253

56.5252

56.5251

56.525

56.5249

56.5248

56.5247

56.5246

56.5245

0 2 4 6 8 10

Time

Fig. 4. Experiment 1: graph of the L 2 -norm of the solution in time

Fig. 5. Experiment 2: the profile of the diffusion factor μ (North pole view). The colour map
ranges from white (maximum) to black (minimum).

where

ξ ≡ ω ( λ − ϑ 1 tan κ 1 ϕ )+ ϑ 2 tan κ 2 ϕ sin γt . (33)

In order for (32) to be the solution to (1), the sources must be

α ∂T
∂λ

2

μT α− 1
R cos ϕ

+ T ∂ 2 T
∂λ 2

∂T
∂t −

1
R cos ϕ

f ( λ, ϕ, t )=

2

T ∂ 2 T + α ∂T

∂ϕ

+ cos ϕ
R ∂ϕ 2 − tan ϕ ∂T

, (34)

∂ϕ