Nonlocal heat flows preserving the L2 energy

Luis Caffarelli, Fanghua Lin

Research output: Contribution to journalArticlepeer-review


We shall study L2 energy conserved solutions to the heat equation. We shall first establish the global existence, uniqueness and regularity of solutions to such nonlocal heat flows. We then extend the method to a family of singularly perturbed systems of nonlocal parabolic equations. The main goal is to show that solutions to these perturbed systems converges strongly to some suitable weak-solutions of the limiting constrained nonlocal heat flows of maps into a singular space. It is then possible to study further properties of such suitable weak solutions and the corresponding free boundary problem, which will be discussed in a forthcoming article.

Original languageEnglish (US)
Pages (from-to)49-64
Number of pages16
JournalDiscrete and Continuous Dynamical Systems
Issue number1-2
StatePublished - Jan 2009


  • Global existence
  • Nonlocal heat equation
  • Singularly perturbed parabolic equations
  • Suitable weak solutions

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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