| Abstract: |
| We study the asymptotic behavior of blowup solutions
for the heat equation with a nonlinear boundary condition
on the half space.
By the presence of nonlinearities on the boundary,
solutions can blow up on the boundary.
It is known that
the singularity of blowup solutions along the direction vertical
to the boundary are determined by unique self-similar solutions.
A goal is to give a complete description of
the singularity on the boundary.
In this talk,
we focus on derivation of the matched asymptotic expansion,
which is a key part in the proof. |
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