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The Dirichlet Problem for the Total Variation Flow

✍ Scribed by F. Andreu; C. Ballester; V. Caselles; J.M. Mazón

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
299 KB
Volume
180
Category
Article
ISSN
0022-1236

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✦ Synopsis

We introduce a new concept of solution for the Dirichlet problem for the total variational flow named entropy solution. Using Kruzhkov's method of doubling variables both in space and in time we prove uniqueness and a comparison principle in L 1 for entropy solutions. To prove the existence we use the nonlinear semigroup theory and we show that when the initial and boundary data are nonnegative the semigroup solutions are strong solutions.

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