Nonlocal heat flows preserving the L2 energy

Luis Caffarelli, Fanghua Lin

Research output: Contribution to journalArticle

Abstract

We shall study L2 energy conserved solutions to the heat equa- tion. We shall first establish the global existence, uniqueness and regularity of solutions to such nonlocal heat flows. We then extend the method to a fam- ily 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- Series A
Volume37
Issue number8
StatePublished - Aug 2017

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Keywords

  • 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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