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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.

3 votes

Question on Parabolic PDEs: Improvement of the bound ${\vert \vert v(\cdot,t)-v_0(\cdot) \ve...

Maybe I'm missing something, but it doesn't seem that your desired inequality can be true (even with the right-hand side of $(*)$ replaced by $C t^{\epsilon}$). It would imply uniform convergence of $ …
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