Optimization of Laplacian Eigenvalues in Perforated Domains and Applications

description to be written; pictures

• Optimizing the Fundamental Neumann Eigenvalue for the Laplacian in a Domain with Small Traps
  with T. Kolokolnikov and M. Titcombe (European J. Appl. Math., Vol. 16, No. 2, (2005), pp. 161-2000.)

• An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part I: Two-Dimensional Domains
  with S. Pillay, A. Peirce, and T. Kolokolnikov (SIAM Multiscale Modeling and Simulation, Vol. 8, No. 3, (2010), pp. 803-835.)

• An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part II: The Sphere
  with A. Cheviakov and R. Straube (SIAM Multiscale Modeling and Simulation, Vol. 8, No. 3, (2010), pp. 836-870.)

• An Asymptotic Analysis of the Persistence Threshold for the Diffusive Logistic Model in Spatial Environments with Localized Patches
  with A. Lindsay (Discrete and Continuous Dynamical Systems Series B, Vol. 14, No. 3, (2010), pp. 1139-1179.)

• Optimizing the Principal Eigenvalue of the Laplacian in a Sphere with Interior Traps
  with A. Cheviakov (Mathematical and Computer Modeling, Vol. 53, Special Issue for the international conference,
  "Mathematical Methods and Modeling of Biological Phenomena", held in Rio de Janiero, (2011), pp. 1394-1409.)

• Mathematical Modeling and Numerical Computation of Narrow Escape Problems
  with A. Cheviakov, A. S. Reimer (submitted, Phys. Rev. E. March (2011), 23 pages).