Differentiability with Respect to Parameters of Weak Solutions of Linear Parabolic Equations

John R. Singler, Missouri University of Science and Technology

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We consider the differentiability of weak solutions of linear parabolic equations with respect to parameters and initial data. under natural assumptions, it is shown that solutions possess as much differentiability with respect to the data as do the terms appearing in the equation. The derivatives are shown to satisfy the appropriate sensitivity equations. The theoretical results are illustrated with an example.