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.