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Differentiability with respect to parameters of weak solutions of linear parabolic equations

✍ Scribed by John R. Singler

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
221 KB
Volume
47
Category
Article
ISSN
0895-7177

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✦ Synopsis

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.

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