Nonlocal heat flows preserving the L2 energy

Luis Caffarelli, Fang-Hua 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 1 2017

Fingerprint

Suitable Weak Solutions
Heat Flow
Heat transfer
Singularly Perturbed Systems
Nonlocal Equations
Existence-uniqueness
Regularity of Solutions
Uniqueness of Solutions
Perturbed System
Free Boundary Problem
Energy
Heat Equation
Global Existence
Parabolic Equation
Existence of Solutions
Limiting
Converge

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Nonlocal heat flows preserving the L2 energy. / Caffarelli, Luis; Lin, Fang-Hua.

In: Discrete and Continuous Dynamical Systems- Series A, Vol. 37, No. 8, 01.08.2017, p. 49-64.

Research output: Contribution to journalArticle

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