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 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
Volume23
Issue number1-2
DOIs
StatePublished - Jan 2009

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
Family

Keywords

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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

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

In: Discrete and Continuous Dynamical Systems, Vol. 23, No. 1-2, 01.2009, p. 49-64.

Research output: Contribution to journalArticle

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