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Questions about partial differential equations of parabolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
2
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long time existence of a nonlinear parabolic equation
I am thinking about a geometric problem which boils down to the following parabolic equation:
Suppose $u=u(r,t)$, $r$ is defined on $[0,1]$ and $t>0$
$$\begin{cases}\displaystyle \frac{\partial u}{\pa …
7
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Reference for Hölder estimate on parabolic equation with Neumann boundary condition
I saw a type of Hölder estimate in Friedman's book: Partial Differential Equations of Parabolic Type (page 200, 3.24) which goes as follows:
Suppose we have a uniformly parabolic equation with Hölder …