Electronic Journal of Differential Equations: Conference 19, 2010.

Proceedings of the Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations, Mississippi State University, USA, May 7-9, 2009.

Foreword

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 five 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. Since 2005, the conference has been organized jointly by Mississippi State University and University of Alabama at Birmingham (UAB) and renamed as the Mississippi State - UAB Conference on Differential Equations and Computational Simulations. The sixth and seventh conferences were held May 13-14, 2005 and November 1-3, 2007, respectively. Special issues of the Journal of Applied Mathematics and Computation (65:1-3, 1994 and 89:1-3, 1998) and the Electronic Journal of Differential Equations (Conference-01, 1997, Conference-03, 1999, Conference-10, 2003, Conference-15, 2007, and Conference-17, 2009) were published as the conference proceedings for refereed papers presented at these conferences.

The eighth conference in this highly successful conference series took place at Mississippi State University on May 7-9, 2009. This conference was dedicated to Joe F. Thompson  who is a William L. Giles Distinguished Professor at Mississippi State University, for his outstanding and continuing contributions to Mississippi State University. There were thirteen invited principal lecturers:

• Doublas Arnold, University of Minnesota, Hilbert Complexes, Finite Element Exterior Calculus, and Applications
• Peter Bates, Michigan State University, Invariant Manifolds for PDEs and the Motion of Particles driven by Allen-Cahn Dynamics
• Jack Benek, Wright-Patterson Air Force Base, Hi Fi Physics Based Research for AF Applications
• Alfonso Castro, Harvey Mudd College, Semilinear Wave Equations with Nonmonotone Nonlinearity
• Pavel Drabek, University of West Bohemia, Czech Republic, Model of Phase Transitions with Nonsmooth Potential: Continua of High Energy Local Minimizers
• Gisele Goldstein, University of Memphis, Modern Boundary Conditions and Their Applications
• Philip Maini, University of Oxford, United Kingdom, Modelling Aspects of Solid Tumour Growth
• Scott Morton, Eglin Air Force Base, A Modular Open System Architecture for Multi-disciplinary Computational Science and Engineering Simulations
• Tinsley Oden, University of Texas at Austin, Validation, Error Estimation, Uncertainty Quantification, and Control of Multiscale Models in Nanomanufacturing
• Stanley Osher, University of California at Los Angeles, New Algorithms in Information Science
• Peter Polacik, University of Minnesota, Singularities of Complex Solutions of Burgers Equation
• Jere Segrest, University of Alabama at Birmingham, Computational Approaches to the Structure and Dynamics of High Density Lipoproteins, a Soft Form of Condensed Matter easily Deformable by Thermal Fluctuations
• Theresa Windus, AMES LAB, U.S. Department of Energy, Monte Carlo Simulations of Cluster Nucleation Using Quantum Mechanical Potentials

In addition, a total of 89 contributed papers were presented during the three day conference. The conference was attended by  147 researchers. The conference participants came from 14 different countries including Australia, Belgium, Bulgaria, Canada, Czech Republic, France, Georgia, Hungary, India, Italy, Saudi Arabia, South Africa, United Kingdom, 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 and diffusion, asymptotic properties, existence and uniqueness, multiplicity and regularity of solutions, quasireversibility for inhomogeneous ill-posed problems in Hilbert space, Lipschitz constants for positive solutions of second order elliptic equations.
2. Computational/Numerical Techniques - Numerical methods involving enthalpy model for heating, melting, and vaporization in laser ablation, time stepping schemes on the cable equation, optimal control of a waste water cleaning plant, convergence of the implicit Lax-Friedrichs numerical discretization scheme for Burgers equation, a hybrid semi-primitive shock capturing scheme for hyperbolic problems, stability and consistency of nonstandard linear-implicit methods for semilinear stochastic heat equations, numerical solution for nonlocal Sobolev-type differential equations, WENO schemes for nonlinear Tricomi equation.
   
3. Mathematical and Computational Biology - Model of the infestation of a honeybee colony by the acute paralysis virus, periodic solutions of a blood cell production model of M.C. Mackey, steady states of a Logistic growth population model with diffusion and constant yield harvesting, compressible fluid flow model with capillary stress effects.
   

We would like to thank the principal speakers and the participants for their valuable contributions to the success of the conference and the publication of this proceedings. We gratefully acknowledge the support provided by the National Science Foundation and the Institute for Mathematics and its Applications at the University of Minnesota. The support from the College of Arts and Sciences, the College of Engineering, the Office of Research and Economic Development, the Department of Mathematics and Statistics, and the Center for Computational Sciences at the High Performance Computing Collaboratory at Mississippi State University and the Department of Mechanical Engineering and the School of Engineering at the University of Alabama at Birmingham are 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 Department of Mathematics University of Tennessee at Chatanooga 415 EMCS Building, Dept 6956 615 McCallie Ave Chattanooga, TN 37403		Roy Koomullil Department of Mechanical Engineering  University of Alabama at Birmingham Hoehn Engineering Building 1075 13th Street South Suite 101 Birmingham, Alabama 35294-4440
	Hyeona Lim Department of Mathematics and Statistics  Mississippi State University 410 Allen Hall Mississippi State, MS 39762-5921		Ratnasingham Shivaji Department of Mathematics and Statistics  Mississippi State University 410 Allen Hall Mississippi State, MS 39762-5921
	Bharat Soni Department of Mechanical Engineering  University of Alabama at Birmingham Hoehn Engineering Building 1075 13th Street South Suite 101 Birmingham, Alabama 35294-4440		Jianping Zhu Department of Mathematics University of Texas at Arlington 411 S. Nedderman Drive 478 Pickard Hall Arlington, Texas 76019-0408

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