The volume is from the proceedings of the international conference held in celebration of Stanley Osher's sixtieth birthday. It presents recent developments and exciting new directions in scientific computing and partial differential equations for time dependent problems and their interplay with other fields, such as image processing, computer vision and graphics. Over the past decade, there have been very rapid developments in the field. This volume emphasizes the strong interaction of advanced mathematics with real-world applications and algorithms.

The book is suitable for graduate students and research mathematicians interested in scientific computing and partial differential equations.

Also available from the AMS are Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering and Combinatorial and Computational Algebra.

Readership

Graduate students and research mathematicians interested in scientific computing and partial differential equations.

Table of Contents

• Y. Brenier -- Systems of particles involving permutations and their continuous limits
• R. E. Caflisch and D. G. Meyer -- A reduced order model for epitaxial growth
• T. F. Chan and J. Shen -- On the role of the BV image model in image restoration
• L.-T. Cheng and W. E -- The heterogeneous multi-scale method for interface dynamics
• A. Ditkowski and D. Gottlieb -- On the Engquist Majda absorbing boundary conditions for hyperbolic systems
• M.-H. Giga and Y. Giga -- Minimal vertical singular diffusion preventing diffusion preventing overturning for the Burgers equation
• K. Harriman, P. Houston, B. Senior, and E. Süli -- $hp$-version discontinuous Galerkin methods with interior penalty for partial differential equations with nonnegative characteristic form
• D. Li and F. J. Hickernell -- Trigonometric spectral collocation methods on lattices
• L. Ju, M. D. Gunzburger, and L. S. Hou -- Approximation of exact boundary controllability problems for the 1-D wave equation by optimization-based methods
• P. Ming and Z.-c. Shi -- Some low order quadrilateral Reissner-Mindlin plate elements
• H. Tang and T. Tang -- Multi-dimensional moving mesh methods for shock computations
• D. D. Vvedensky, C. Baggio, A. Chua, C. Haselwandter, and R. Vardavas -- Stochastic differential equations for driven lattice systems
• T. Yabe, K. Takizawa, F. Xiao, and A. Ikehata -- Universal solver CIP for all phases of matter