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.
J. R. Singler, "Differentiability with Respect to Parameters of Weak Solutions of Linear Parabolic Equations," Mathematical and Computer Modelling, Elsevier, Jan 2007.
The definitive version is available at https://doi.org/10.1016/j.mcm.2007.02.022
Mathematics and Statistics
United States. Air Force. Office of Scientific Research
United States. Defense Advanced Research Projects Agency. Special Projects Office
Keywords and Phrases
Frechet Differentiability; Linear Parabolic Equations; Parameters; Weak Solutions
International Standard Serial Number (ISSN)
Article - Journal
© 2007 Elsevier, All rights reserved.
01 Jan 2007