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2009, Volume 23, Issue 1&2: 49-64. Doi: 10.3934/dcds.2009.23.49
This issue Previous Article On the convergence of viscous approximations after shock interactions Next Article Robust filtering for joint state-parameter estimation in distributed mechanical systems

Nonlocal heat flows preserving the L2 energy

  • 1.

    Department of Mathematics, University of Texas at Austin, 1 University Station, C1200, Austin, TX 78712-1082

  • 2.

    Department of Mathematics, New York University, 251 Mercer St. New York, NY 10012

Received:  October 31, 2007
Revised:  March 31, 2008
Published:  April 2009
Abstract Related Papers Cited by
    Abstract
  • We shall study L2 energy conserved solutions to the heat equation.We shall first establish the global existence, uniqueness andregularity of solutions to such nonlocal heat flows. We then extend themethod to a family of singularly perturbed systems of nonlocal parabolicequations. The main goal is to show that solutions to these perturbedsystems converges strongly to some suitable weak-solutionsof the limiting constrained nonlocal heat flows of maps into a singularspace. It is then possible to study further properties of such suitableweak solutions and the corresponding free boundary problem, which willbe discussed in a forthcoming article.
    Mathematics Subject Classification: Primary: 35K05, 35K55; Secondary: 49N60.

    Citation:
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