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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

5 votes
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196 views

Asymptotic higher order derivative estimates for solutions of semi-linear parabolic PDEs

Question: Consider a semi-linear parabolic equation on a bounded domain $\Omega \subset \mathbb{R}^m$: $$ \frac{\partial f_t}{\partial t} = -\Delta f_t + Q(f_t, df_t), $$ with smooth initial data …
Marco Spinaci's user avatar