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fix doc
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mbouyges committed Jun 18, 2024
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9 changes: 6 additions & 3 deletions src/example/heat_equation_sphere/heat_equation_sphere.jl
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Expand Up @@ -2,11 +2,14 @@ module HeatEquationSphere #hide
# # Heat equation on a sphere
# Adapted from https://www.chebfun.org/examples/sphere/SphereHeatConduction.html.
# The equation solved on the sphere is
# $$
# ```math
# \partial_t T = \alpha \Delta_\Gamma T
# $$
# ```
# The temperature is initialized by
# the following sum of spherical harmonic: $u(\lambda, \theta) = Y^0_6(\lambda, \theta) + \sqrt{14/11}Y^6_6(\lambda,\theta)$,
# the following sum of spherical harmonic:
# ```math
# u(\lambda, \theta) = Y^0_6(\lambda, \theta) + \sqrt{14/11}Y^6_6(\lambda,\theta)
# ```
# where $\lambda$ and $\theta$ are two angles parametrizing the sphere.
# Hence an analytical solution can be found : $u(\lambda,\theta, t) = e^{-42 \alpha t} u_0(\lambda, \theta)$.
#
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