Matthew Lorig, Stefano Pagliarani, Andrea Pascucci
Published 2013-12-11, updated 2014-11-28Version 2
We consider the Cauchy problem associated with a general parabolic partial differential equation in $d$ dimensions. We find a family of closed-form asymptotic approximations for the unique classical solution of this equation as well as rigorous short-time error estimates. Using a boot-strapping technique, we also provide convergence results for arbitrarily large time intervals.
On Second Order Elliptic and Parabolic Equations of Mixed Type
Regularity theory for parabolic equations with singular degenerate coefficients
Quantitative stochastic homogenization and regularity theory of parabolic equations
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