Abstract
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.
Recommended Citation
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
Department(s)
Mathematics and Statistics
Sponsor(s)
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)
0895-7177
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2007 Elsevier, All rights reserved.
Publication Date
01 Jan 2007
