Research

My research area of interest lies in Applied Mathematics and Analysis. In particular, my work focuses on the analysis of nonlinear evolutionary partial differential equations (PDEs). I am interested in the classes of PDEs that describe several physical phenomena such as acoustic pressure waves, mechanical vibrations of plates and shells, and viscoelastic materials with memory. I am mainly concerned with questions dealing with local and global existence, blow-up, and long time behavior of solutions.

Publications

Here is a list of my publications. They are also accessible via MathSciNet or Google Scholar Citation.

Ph.D. Students

• Keith Agre, Ph.D. 2000, Department of Mathematics, St. Cloud State University, St. Cloud, Minnesota.
• Theresa Jorgensen, Ph.D. 2000, Department of Mathematics, University of Texas at Arlington, Arlington, Texas.
• Sawanya Sakuntasathien, Ph.D. 2008, Mathematics Department, Faculty of Science, Silpakorn University, Nakhonpathom, Thailand.
• Zahava Wilstein, Ph.D. 2011, Department of Mathematics and Computer Science, Berry College, Mount Berry, Georgia.
• Yanqiu Guo, Ph.D. 2012, Department of Mathematics & Statistics, Florida International University, Miami, Florida.
• Pei Pei, Ph.D. 2014, Department of Mathematics, Otterbein University, Westerville, Ohio.
• Nicholas Kass, Ph.D. 2018, Department of Mathematics, University of Nebraska-Omaha, Omaha, Nebraska.
• Andrew Becklin, Ph.D. 2020, Department of Mathematics, Drake University, Des Moines, Iowa.
• Dylan McKnight, Ph.D. 2024, (co-advised with George Avalos), Department of Mathematics & Statistics, Colorado Mesa University, Mesa, Colorado.

Awards

• The College Distinguished Teaching Award, 2003.
• The Recognition Award for Contribution to Students from the UNL Parents Association and the Teaching Council, received 13 times.

Items of Interest to Students in Some Mathematics Courses

If you love working on some challenging problems in calculus, click here.
To learn more about Mathematical Genealogy, click here.

Arabic & Irish Quotes

You'll never plow a field by turning it over in your mind.