Abstract
In this note we come back to face a problem regarding forward-backward parabolic equations like $(r(x,t) u)_t - u_{xx} = 0$ and $r(x,t) u_t - u_{xx} = 0$ ($r$ is both positive and negative): the continuity of $t \mapsto \int u^2(x,t) |r(x,t)| \, dx$.
Citation
Fabio Paronetto. "An apparently unnatural estimate about forward-backward parabolic equations." Adv. Differential Equations 26 (3/4) 133 - 162, March/April 2021. https://doi.org/10.57262/ade026-0304-133
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