Gradient Flow - Definition and Sources

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SUMMARY

The discussion centers on the concept of "gradient flow of a functional," specifically characterized by the equation Du / Dt = P u, where P is a differential operator linked to the Euler-Lagrange equation of the functional F(u). The original poster expresses difficulty in finding elementary materials on this topic and seeks recommendations for foundational reading. A suggested resource is the preprint by Daneri and Savare, which may provide valuable insights into the subject.

PREREQUISITES
  • Understanding of functional analysis
  • Familiarity with differential equations
  • Knowledge of the Euler-Lagrange equation
  • Basic concepts of calculus of variations
NEXT STEPS
  • Read the preprint "Gradient Flows in Metric Spaces and in the Space of Probability Measures" by Daneri and Savare
  • Study the Euler-Lagrange equation in detail
  • Explore the calculus of variations and its applications
  • Investigate advanced topics in functional analysis related to gradient flows
USEFUL FOR

Researchers, mathematicians, and students in applied mathematics or theoretical physics who are interested in the mathematical foundations of gradient flows and their applications in variational problems.

muzialis
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Hi all,

I am struggling to find any elementary material on the "gradient flow of a functional" concept.

From introductions in advanced papers I seem to have understood that, assigned a functional F (u), the gradient flow is charactwerized by an equation of the type Du / Dt = P u , where P is a differential operator related to the functional's Euler- Lagrange equation.

I would like to understand more, but was surpsrisngly unable to find any sources on the Internet.
Can anybody suggest a good starting reading?

Many thanks for any help
 
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