Electronic Journal of Differential Equations: Conference 17, 2009.

Proceedings of the Seventh Mississippi State - UAB Conference on Differential Equations and Computational Simulations, Doubletree Hotel, Birmingham, Alabama, USA. November 1-3, 2007.

Foreword

Mathematical modeling, analysis, and computational simulations have fundamentally changed how complex phenomena in sciences and engineering are analyzed and investigated. Gone are the days when mathematicians could work individually in closed offices using pencil and paper to solve simple model problems. A successful effort in modeling, analysis, and simulations for real-world applications now requires a truly interdisciplinary collaboration among mathematicians, computer scientists, and researchers in various scientific and engineering fields. To provide a joint forum for mathematicians, scientists, and engineers from industries, federal laboratories, and academia to exchange ideas and present the latest research progresses, a conference series on Differential Equations and Computational Simulations was started in 1993 by the Department of Mathematics and Statistics and the NSF Engineering Research Center at Mississippi State University. An overall goal of this conference series is to promote interdisciplinary research collaborations and education effort in mathematical and computational analyses of differential equations with real-world applications.

The first six Mississippi State Conferences on Differential Equations and Computational Simulations were held March 19-20, 1993, April 7-8, 1995, May 16-17, 1997, May 21 - 22, 1999, May 18 - 19, 2001, and May 13-14, 2005. Special issues of the Journal of Applied Mathematics and Computation (65:1-3, 1994 and 89:1-3, 1998) and of the Electronic Journal of Differential Equations (Conference-01, 1997, Conference-03, 1999, Conference-10, 2003, and Conference-15, 2007) were published as the conference proceedings for refereed papers presented at these conferences.

The seventh conference in this highly successful conference series took place in Birmingham, Alabama, November 1-3, 2007. The conference was organized jointly by Mississippi State University and University of Alabama at Birmingham (UAB), and was renamed as Mississippi State - UAB Conference on Differential Equations and Computational Simulations. There were twelve invited principal lectures:

• Oscar Bruno, California Institute of Technology, Fast High-Order High-Frequency Solvers in Computational Acoustics and Electromagnetics
• Chris Cosner, University of Miami, Mathematical Aspects of the Ideal Free Distribution
• Jeff Crandall, University of Virginia, Computational Models? Pushing or Pulling the Realm of Experimental Biomechanics?
• Norman Dancer, University of Sydney, Australia, Finite Morse Index Solutions and the Branch of Positive Solutions of Exponential Problems
• Joshua Epstein, The Brookings Institution, Coupled Contagion Dynamics of Fear and Disease: Mathematical and Computational Explorations
• Lisa Fauci, Tulane University, Mathematical Models of the Biofluidmechanics of Reproduction
• YanYan Li, Rutgers University, Gradient Estimates for Elliptic Equations and Systems from Composite Material
• Jean Mawhin, University of Catholique de Louvain, Belgium, Bounded Solutions: Differential vs Difference Equations
• Charles Nietubicz, Army research Laboratory, High Performance Computing at the Army Research Laboratory - Impact of Cluster technology
• Jaime Peraire, Massachusetts Institute of Technology, High Order Discontinuous Galerkin Methods for Aerodynamics
• John Rice, IBM TJ Watson Research Center, ODE-based Multiscale Approach to Modeling Cardiac Contraction
• Peter Takac, University of Rostock, Germany, Two Variational Problems with the p-Laplacian: a Stationary Cahn-Hilliard Model and the Fredholm Alternative near the First Eigenvalue

In addition, a total of 95 contributed papers were presented during the three-day conference. The conference was attended by 131 researchers. The conference participants came from Australia, Belgium, Canada, China, Czech Republic, Germany, Korea, and the United States.

The papers in this special issue of EJDE represent a broad range of research in the following multidisciplinary areas:

1. Mathematical Analysis and Bifurcation Theory - Ordinary and partial differential equations involving reaction-diffusion, asymptotic properties, existence and uniqueness, multiplicity and regularity of solutions.
2. Computational/Numerical Techniques - Numerical methods involving isobaric compositional thermal model for methane hydrate formation and decomposition, high order model for image denoising, multilevel adaptive mesh generation scheme, spectral element simulations for a single-phase fluid flow problem, optimized multidimensional difference schemes for multidimensional hyperbolic partial differential equations, domain decomposition method for coupled flow-structure-thermal interaction problems.
3. Computational Biology - Bioclogging models for spatial expansion of the bacterial population, coupled flow interaction transport models for blood and plasma flow, gene activation model for cytokine production.

We would like to thank the participants and principal speakers for their valuable contributions to the success of the conference and publication of the proceedings. We gratefully acknowledge the support provided by the National Science Foundation and the Institute for Mathematics and its Applications at University of Minnesota. The support from the College of Arts and Sciences, the College of Engineering, the Office of Research, the Department of Mathematics and Statistics, and the Center for Computational Sciences at the High Performance Computing Collaboratory at Mississippi State University is also acknowledged. We also greatly appreciate the Electronic Journal of Differential Equations and Atlas Conferences for their support. Last but not least, we appreciate very much the diligence and responsiveness of the reviewers of the manuscripts that made the publication of this proceedings possible.

Special Issue Editors:
Main Editors: John Graef (University of Tennessee at Chatanooga), Roy Koomullil (University of Alabama at Birmingham), Hyeona Lim (Mississippi State University), Ratnasingham Shivaji (Mississippi State University), Bharat Soni (University of Alabama at Birmingham), Jianping Zhu (University of Texas at Arlington).
Associate Editors: Alfonso Castro (Harvey Mudd College), Gary Cheng (University of Alabama at Birmingham), Maya Chhetri (University of North Carolina at Greensboro), Hai Dang (Mississippi State University), Seongjai Kim (Mississippi State University), Ian Knowles (University of Alabama at Birmingham), David Littlefield (University of Alabama at Birmingham), Seth Oppenheimer (Mississippi State University), Chuanxi Qian (Mississippi State University), Mohsen Razzaghi (Mississippi State University), Alan Shih (University of Alabama at Birmingham), James Ward (University of Alabama at Birmingham), Xiangsheng Xu (Mississippi State University).

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