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Results tagged with parabolic-pde
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user 88462
Questions about partial differential equations of parabolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
1
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Does $\int_0^t \Vert u_x(s,\cdot) \Vert_{L^2} ds \le C$ imply $\Vert u_x (t,\cdot) \Vert_{L^...
In the case of linear heat equation, we write
$$ u(x,t) = \int_{\mathbb{R}} \Gamma(x-y,t) u_0(y) dy.$$
Here $\Gamma(x,t)$ is the standard heat kernel. Note that
$$ \left|\left(\frac{\partial}{\partial …
- 323
1
vote
Parabolic Sobolev inequality in Sobolev mixed norm spaces
You can find a proof in Corollary 5.3 in Krylov's On parabolic Adams's, the Chiarenza-Frasca theorems, and some other results related to parabolic Morrey spaces (Link)
Here is also a link to the PDF o …
- 323