Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow

Title:

Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow

Creator:

Boussandel, Sahbi, Chill, Ralph, and Fašangová, Eva

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:e7a370d7-9803-4bd4-ba47-775f07f30520
uuid:e7a370d7-9803-4bd4-ba47-775f07f30520

Subject:

curve shortening flow, maximal regularity, and local inverse function theorem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Local well-posedness of the curve shortening flow, that is, local existence, uniqueness and smooth dependence of solutions on initial data, is proved by applying the Local Inverse Function Theorem and $L^2$-maximal regularity results for linear parabolic equations. The application of the Local Inverse Function Theorem leads to a particularly short proof which gives in addition the space-time regularity of the solutions. The method may be applied to general nonlinear evolution equations, but is presented in the special situation only.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

335-346

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:2

Harvested from:

CDK

Metadata only:

false